####################################################################### # # A 'most efficient" Runge--Kutta (16:9(8)) pair # # These are approximate REAL coefficients # computed using MAPLE with 40 digits for # # a SIXTEEN-stage conventional pair methods of # orders p=8 and p=9, with dominant # stage order = 5, # # together with approximate coefficients # # for two interpolants of orders 8 and 9 # # which require 5 and 5 extra stages respectively. # (Companion files list COEFFICIENTS of the pair as exact # RADICALS, and 40-digit floating point approximations # otherwise.) # # This procedure is "most efficient" in the sense that # for a specified maximum coefficient from b and A, # it has a propagating formula which almost minimizes # the 2-norm of the local truncation error as # # T10,2 ~ .0000003490 # # (Formulas with slightly different nodes c_i can # have a slightly smaller error norm perhaps # achieved by having a larger maximum coefficient.) # # Additional stages and interpolating weights allow # for the computation of an approximation at any # point of the domain of solution of order up to p. # These interpolants have continuous derivatives. # # Nodes c[17]=1, c[18] - c[21] were selected in an # attempt to minimize the maximum of the 2-norm of # the local truncation error over the interval [0,1] # for the interpolant of order 8, and this value is # # T_92 ~ .0000007396 # # This 2-norm has four local maximum values on [0,1]. # # The remaining five nodes were selected in an attempt # to minimize the maximum of the 2-norm of the local # truncation error on the interval [0,1] for the # interpolant of order 9, and this value is # # T_10,2 ~ .0000003490, # # the endpoint 2-norm error. This 2-norm is monotone # increasing on [0,1]. # # The formulas scanned for this optimal formula are # those developed in J.H. Verner, SIAM NA 1978, 772-790, # "Explicit Runge--Kutta methods with estimates of the # Local Truncation Error". It is conceivable that the # pairs in J.H. Verner, Applied Numerical Mathematics 22 # 1996, 345--357, "High-order explicit Runge--Kutta pairs # with low stage order", which also require 16 stages, # but solve the order conditions in a different way # may yield particular pairs of equivalant or more # efficiency. # ###################################################################### # # NODES # ----- c[1] = 0. c[2] = .3462e-1 c[3] = .9702435063878044594828361677100617517633e-1 c[4] = .1455365259581706689224254251565092627645 c[5] = .561 c[6] = .2290079115904850126662751771814700052182 c[7] = .5449920884095149873337248228185299947818 c[8] = .645 c[9] = .4837500000000000000000000000000000000000 c[10] = .6757e-1 c[11] = .2500 c[12] = .6590650618730998549405331618649220295334 c[13] = .8206 c[14] = .9012 c[15] = 1. c[16] = 1. # #********************************************************* # NEW COUPLING COEFFICIENTS # --------------------- c[1] = 0. # c[2] = .3462e-1 a[2,1] = .3462e-1 # c[3] = .9702435063878044594828361677100617517633e-1 a[3,1] = -.389335438857287327017042687229284478532e-1 a[3,2] = .1359578945245091786499878854939346230295 # c[4] = .1455365259581706689224254251565092627645 a[4,1] = .3638413148954266723060635628912731569111e-1 a[4,2] = 0. a[4,3] = .1091523944686280016918190688673819470733 # c[5] = .561 a[5,1] = 2.025763914393969636805657604282571047511 a[5,2] = 0. a[5,3] = -7.638023836496292020387602153091964592952 a[5,4] = 6.173259922102322383581944548809393545442 # c[6] = .2290079115904850126662751771814700052182 a[6,1] = .5112275589406060872792270881648288397197e-1 a[6,2] = 0. a[6,3] = 0. a[6,4] = .1770823794555021537929910813839068684087 a[6,5] = .80277624092225014536138698108025283759e-3 # c[7] = .5449920884095149873337248228185299947818 a[7,1] = .1316006357975216279279871693164256985334 a[7,2] = 0. a[7,3] = 0. a[7,4] = -.2957276252669636417685183174672273730699 a[7,5] = .878137803564295237421124704053886667082e-1 a[7,6] = .6213052975225274774321435005639430026100 # c[8] = .645 a[8,1] = .7166666666666666666666666666666666666667e-1 a[8,2] = 0. a[8,3] = 0. a[8,4] = 0. a[8,5] = 0. a[8,6] = .3305533578915319409260346730051472207728 a[8,7] = .2427799754418013924072986603281861125606 # c[9] = .4837500000000000000000000000000000000000 a[9,1] = .7180664062500000000000000000000000000000e-1 a[9,2] = 0. a[9,3] = 0. a[9,4] = 0. a[9,5] = 0. a[9,6] = .3294380283228177160744825466257672816401 a[9,7] = .1165190029271822839255174533742327183599 a[9,8] = -.3401367187500000000000000000000000000000e-1 # c[10] = .6757e-1 a[10,1] = .4836757646340646986611287718844085773549e-1 a[10,2] = 0. a[10,3] = 0. a[10,4] = 0. a[10,5] = 0. a[10,6] = .3928989925676163974333190042057047002852e-1 a[10,7] = .1054740945890344608263649267140088017604 a[10,8] = -.2143865284648312665982642293830533996214e-1 a[10,9] = -.1041229174627194437759832813847147895623 # c[11] = .25 a[11,1] = -.2664561487201478635337289243849737340534e-1 a[11,2] = 0. a[11,3] = 0. a[11,4] = 0. a[11,5] = 0. a[11,6] = .3333333333333333333333333333333333333333e-1 a[11,7] = -.1631072244872467239162704487554706387141 a[11,8] = .3396081684127761199487954930015522928244e-1 a[11,9] = .1572319413814626097110769806810024118077 a[11,10] = .2152267478031879552303534778794770376960 # c[12] = .6590650618730998549405331618649220295334 a[12,1] = .3689009248708622334786359863227633989718e-1 a[12,2] = 0. a[12,3] = 0. a[12,4] = 0. a[12,5] = 0. a[12,6] = -.1465181576725542928653609891758501156785 a[12,7] = .2242577768172024345345469822625833796001 a[12,8] = .2294405717066072637090897902753790803034e-1 a[12,9] = -.35850052905728761357394424889330334334e-2 a[12,10] = .8669223316444385506869203619044453906053e-1 a[12,11] = .4383840651968337846196219974168630120572 # c[13] = .8206 a[13,1] = -.4866012215113340846662212357570395295088 a[13,2] = 0. a[13,3] = 0. a[13,4] = 0. a[13,5] = 0. a[13,6] = -6.304602650282852990657772792012007122988 a[13,7] = -.281245618289472564778284183790118418111 a[13,8] = -2.679019236219849057687906597489223155566 a[13,9] = .518815663924157511565311164615012522024 a[13,10] = 1.365353187603341710683633635235238678626 a[13,11] = 5.885091088503946585721274891680604830712 a[13,12] = 2.802808786272062889819965117517532194812 # c[14] = .9012 a[14,1] = .4185367457753471441471025246471931649633 a[14,2] = 0. a[14,3] = 0. a[14,4] = 0. a[14,5] = 0. a[14,6] = 6.724547581906459363100870806514855026676 a[14,7] = -.425444280164611790606983409697113064616 a[14,8] = 3.343279153001265577811816947557982637749 a[14,9] = .617081663117537759528421117507709784737 a[14,10] = -.929966123939932833937749523988800852013 a[14,11] = -6.099948804751010722472962837945508844846 a[14,12] = -3.002206187889399044804158084895173690015 a[14,13] = .2553202529443445472336424602988558373637 # c[15] = 1. a[15,1] = -.779374086122884664644623040843840506343 a[15,2] = 0. a[15,3] = 0. a[15,4] = 0. a[15,5] = 0. a[15,6] = -13.93734253810777678786523664804936051203 a[15,7] = 1.252048853379357320949735183924200895136 a[15,8] = -14.69150040801686878191527989293072091588 a[15,9] = -.494705058533141685655191992136962873577 a[15,10] = 2.242974909146236657906984549543692874755 a[15,11] = 13.36789380382864375813864978592679139881 a[15,12] = 14.39665048665068644512236935340272139005 a[15,13] = -.7975813331776800379127866056663258667437 a[15,14] = .4409353709534277758753793068298041158235 # c[16] = 1. a[16,1] = 2.058051337466886442151242368989994043993 a[16,2] = 0. a[16,3] = 0. a[16,4] = 0. a[16,5] = 0. a[16,6] = 22.35793772796803295519317565842520212899 a[16,7] = .90949810997556332745009198137971890783 a[16,8] = 35.89110098240264104710550686568482456493 a[16,9] = -3.442515027624453437985000403608480262211 a[16,10] = -4.865481358036368826566013387928704014496 a[16,11] = -18.90980381354342625688427480879773032857 a[16,12] = -34.26354448030451782929251177395134170515 a[16,13] = 1.264756521695642578827783499806516664686 a[16,14] = 0. a[16,15] = 0. # #********************************************************* # High order weights c[`, 17] = 1 # ----------------------------------------------------------- # b[1] = .1461197685842315252051541915018784713459e-1 b[2] = 0. b[3] = 0. b[4] = 0. b[5] = 0. b[6] = 0. b[7] = 0. b[8] = -.3915211862331339089410228267288242030810 b[9] = .2310932500289506415909675644868993669908 b[10] = .1274766769992852382560589467488989175618 b[11] = .2246434176204157731566981937082069688984 b[12] = .5684352689748512932705226972873692126743 b[13] = .5825871557215827200814768021863420902155e-1 b[14] = .1364317403482215641609022744494239843327 b[15] = .3057013983082797397721005067920369646664e-1 b[16] = 0. # #********************************************************* # Low order weights C[extra]:= `, 1 # -------------------------------------------------- # bh[1] = .1996996514886773085518508418098868756464e-1 bh[2] = 0. bh[3] = 0. bh[4] = 0. bh[5] = 0. bh[6] = 0. bh[7] = 0. bh[8] = 2.191499304949330054530747099310837524864 bh[9] = .8857071848208438030833722031786358862953e-1 bh[10] = .1140560234865965622484956605091432032674 bh[11] = .2533163805345107065564577734569651977347 bh[12] = -2.056564386240941011158999594595981300493 bh[13] = .3408096799013119935160094894224543812830 bh[14] = 0. bh[15] = 0. bh[16] = .4834231373823958314376726739772871714902e-1 # #******************************************************** # # Largest coefficient in b or A has magnitude `, 35.89110 # #******************************************************** # SUMMARY OF NORMS OF ERRORS: A101, A102, A10inf # ---------------------------------------------------- # A_[10, 1] = `, .6203740397e-5 # A_[10, 2] = `, .3490533482e-6 # A_[10,oo] = `, .6336460338e-7 #***************************************************** # # END OF GENERATION OF A PAIR OF RK METHODS # # ############################################################# # # START OF GENERATION OF STABILITY INTERVALS # # ############################################################# # # Stability Boundaries of High Order Method # ----------------------------------------- # Real Stability Interval is nearly [`, -4.476172723, `,0] # # Stability Boundaries of Low Order Method # ---------------------------------------- # Real Stability Interval is nearly [`, -3.879356943, `,0] # # ############################################################# # # START OF GENERATION OF INTERPOLANT # #******************************************************* # # FIVE ADDITIONAL STAGES FOR INTERPOLANT OF ORDER 8 # c[17] = 1.0 a[17,1] = .1461197685842315252051541915018784713459e-1 a[17,2] = 0. a[17,3] = 0. a[17,4] = 0. a[17,5] = 0. a[17,6] = 0. a[17,7] = 0. a[17,8] = -.3915211862331339089410228267288242030810 a[17,9] = .2310932500289506415909675644868993669908 a[17,10] = .1274766769992852382560589467488989175618 a[17,11] = .2246434176204157731566981937082069688984 a[17,12] = .5684352689748512932705226972873692126743 a[17,13] = .5825871557215827200814768021863420902155e-1 a[17,14] = .1364317403482215641609022744494239843327 a[17,15] = .3057013983082797397721005067920369646664e-1 a[17,16] = 0. # #******************************************************** # # Coupling coefficients for c[18] = .7404185470631561083004100761798676215811 # ---------------------------------------------------- a[18,1] = .1549973668189559302279946863304789372788e-1 a[18,2] = 0. a[18,3] = 0. a[18,4] = 0. a[18,5] = 0. a[18,6] = 0. a[18,7] = 0. a[18,8] = .3355153219059635054403439303177105512242 a[18,9] = .2003613944191860651552622660712101217322 a[18,10] = .1252060659283549312946162355194540994211 a[18,11] = .2298676393184206750544046308957155868736 a[18,12] = -.2020250653476181447824906889122391003637 a[18,13] = .5917103230665456601422111997583025339897e-1 a[18,14] = -.2651834783047638681693835956996437528251e-1 a[18,15] = -.2384094602130971415278110567256446033405e-1 a[18,16] = 0. a[18,17] = .2718171570208501807097257892166705118335e-1 # #******************************************************** # # Coupling coefficients for c[19] = .888 # ---------------------------------------------------- a[19,1] = .1302453943114338366054520296881099431474e-1 a[19,2] = 0. a[19,3] = 0. a[19,4] = 0. a[19,5] = 0. a[19,6] = 0. a[19,7] = 0. a[19,8] = -.7452850902413112085299330666038981625179 a[19,9] = .2643867896429300961465132150322749722129 a[19,10] = .1313961758372753932588328082078842388890 a[19,11] = .2167253815122927263092467187957410643315 a[19,12] = .8734117564076052559016338094938888451419 a[19,13] = .1185905643935776688228545787724340848142e-1 a[19,14] = .5876002941689550612992712203494447529933e-1 a[19,15] = .3266518630202087866399279690939423159022e-2 a[19,16] = 0. a[19,17] = -.8959308648417929824525368306101792182274e-2 a[19,18] = .6941415157202692219907482080827253287034e-1 # #******************************************************** # # Coupling coefficients for c[20] = .696 # ---------------------------------------------------- a[20,1] = .1397089996925942721283716334050740168797e-1 a[20,2] = 0. a[20,3] = 0. a[20,4] = 0. a[20,5] = 0. a[20,6] = 0. a[20,7] = 0. a[20,8] = -.4665765335957674596054673402956853940520 a[20,9] = .2416372787216257077935214889875485248580 a[20,10] = .1290363341345674735721677437066933999929 a[20,11] = .2216700671735105311080225734522323922813 a[20,12] = .6257275123364644931771253383573999863003 a[20,13] = .4355312415679284117869124964829805160429e-1 a[20,14] = .1011962491667290833450024852274278874501 a[20,15] = .1808582254679721049279369742685497400353e-1 a[20,16] = 0. a[20,17] = -.2079875587689169691156509689282083267654e-1 a[20,18] = -.9022232517086218976198252891464664868640e-1 a[20,19] = -.1212796735622254216011467740438097427634 # #******************************************************** # # Coupling coefficients for c[21] = .487 # ---------------------------------------------------- a[21,1] = .1604638888318112738641232352800290501904e-1 a[21,2] = 0. a[21,3] = 0. a[21,4] = 0. a[21,5] = 0. a[21,6] = 0. a[21,7] = 0. a[21,8] = .9517712399458336651642257453589397190702e-1 a[21,9] = .1359187264655317806136927180199100622471 a[21,10] = .1237765280959854006935081364365637515893 a[21,11] = .2335656264102966047058755123098072346246 a[21,12] = -.9051508172625873314662090873741762206189e-1 a[21,13] = -.2537574270006131028513276914038326155331e-1 a[21,14] = -.1359631696887162048002744757083947500478 a[21,15] = -.4679214284145113075088049469061349990847e-1 a[21,16] = 0. a[21,17] = .5177958859391748239949773879090325427473e-1 a[21,18] = .9672595677476773313884172931875718705561e-1 a[21,19] = .1477312690340742769720989417101989769314 a[21,20] = -.1150750712958503934434410263732282100773 # -------------------------------------------------------- # COEFFICIENTS FOR INTERPOLANT bi8 WITH 21 STAGES # -------------------------------------------------------- # # COEFFICIENTS OF bi8[1] bi8[1,1] = 1. u bi8[1,2] = -12.74966541771576102412726774271024205003 u^2 bi8[1,3] = 68.53080766672322360449931519438662010864 u^3 bi8[1,4] = -194.8119745354184115708662255742713867869 u^4 bi8[1,5] = 317.8426371352858465721400485549409045261 u^5 bi8[1,6] = -299.7155409593396451474764978718840789438 u^6 bi8[1,7] = 152.1119186420412302044289062135608459907 u^7 bi8[1,8] = -32.19357055471805948607776335487247499763 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[2] bi8[2,1] = 0. u bi8[2,2] = 0. u^2 bi8[2,3] = 0. u^3 bi8[2,4] = 0. u^4 bi8[2,5] = 0. u^5 bi8[2,6] = 0. u^6 bi8[2,7] = 0. u^7 bi8[2,8] = 0. u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[3] bi8[3,1] = 0. u bi8[3,2] = 0. u^2 bi8[3,3] = 0. u^3 bi8[3,4] = 0. u^4 bi8[3,5] = 0. u^5 bi8[3,6] = 0. u^6 bi8[3,7] = 0. u^7 bi8[3,8] = 0. u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[4] bi8[4,1] = 0. u bi8[4,2] = 0. u^2 bi8[4,3] = 0. u^3 bi8[4,4] = 0. u^4 bi8[4,5] = 0. u^5 bi8[4,6] = 0. u^6 bi8[4,7] = 0. u^7 bi8[4,8] = 0. u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[5] bi8[5,1] = 0. u bi8[5,2] = 0. u^2 bi8[5,3] = 0. u^3 bi8[5,4] = 0. u^4 bi8[5,5] = 0. u^5 bi8[5,6] = 0. u^6 bi8[5,7] = 0. u^7 bi8[5,8] = 0. u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[6] bi8[6,1] = 0. u bi8[6,2] = 0. u^2 bi8[6,3] = 0. u^3 bi8[6,4] = 0. u^4 bi8[6,5] = 0. u^5 bi8[6,6] = 0. u^6 bi8[6,7] = 0. u^7 bi8[6,8] = 0. u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[7] bi8[7,1] = 0. u bi8[7,2] = 0. u^2 bi8[7,3] = 0. u^3 bi8[7,4] = 0. u^4 bi8[7,5] = 0. u^5 bi8[7,6] = 0. u^6 bi8[7,7] = 0. u^7 bi8[7,8] = 0. u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[8] bi8[8,1] = 0. u bi8[8,2] = 141.0696092533712605710078918334708622849 u^2 bi8[8,3] = -1283.768450646593611469556198945305487267 u^3 bi8[8,4] = 4630.280061766681019456906394425884505766 u^4 bi8[8,5] = -8648.500976100316056391914391739346002386 u^5 bi8[8,6] = 8890.812161067019054072477301499300549282 u^6 bi8[8,7] = -4787.949212676938594146631544372229445471 u^7 bi8[8,8] = 1057.665286150543793998769524471496193587 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[9] bi8[9,1] = 0. u bi8[9,2] = -51.75101323451538200013913368910238945675 u^2 bi8[9,3] = 486.0412507312931363219502660627455126442 u^3 bi8[9,4] = -1777.475586368523869187924524440189207548 u^4 bi8[9,5] = 3345.498238649791484065923838383080369426 u^5 bi8[9,6] = -3455.762480007366110892744664331997981283 u^6 bi8[9,7] = 1867.081161290311461863227123612293652933 u^7 bi8[9,8] = -413.4004778109617695287019380323430573493 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[10] bi8[10,1] = 0. u bi8[10,2] = 16.32082008695896537661978157425676142665 u^2 bi8[10,3] = -118.7072740966746629137122793258036781419 u^3 bi8[10,4] = 379.8980653294655976666790006724113822620 u^4 bi8[10,5] = -659.1980179681815547557635890342282178072 u^5 bi8[10,6] = 645.0127094968870314571906430728856355521 u^6 bi8[10,7] = -335.3923630294779850989153429752631332406 u^7 bi8[10,8] = 72.19353685802189350615784496249014886653 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[11] bi8[11,1] = 0. u bi8[11,2] = -5.897787927512737700004074981094546266733 u^2 bi8[11,3] = 89.61427156602281202549839530979318529349 u^3 bi8[11,4] = -381.3887877052766946040448187450031021400 u^4 bi8[11,5] = 773.0964199867749581865429091250468401092 u^5 bi8[11,6] = -834.1212536283262120951621382995179788432 u^6 bi8[11,7] = 463.6209151933600203046608830911748528029 u^7 bi8[11,8] = -104.6991340674217303443344573066910439868 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[12] bi8[12,1] = 0. u bi8[12,2] = -211.5753578293942678386576895806496541353 u^2 bi8[12,3] = 1922.149747207956657441031349510100069933 u^3 bi8[12,4] = -6927.544647063403206822988172864704814066 u^4 bi8[12,5] = 12933.89131149183768334045388734576967421 u^5 bi8[12,6] = -13292.72252236109238830196845558874371599 u^6 bi8[12,7] = 7157.200591588665684047481512110694194478 u^7 bi8[12,8] = -1580.830687765595310572081908235178385210 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[13] bi8[13,1] = 0. u bi8[13,2] = -29.64315154973386448483853503830022916124 u^2 bi8[13,3] = 265.6161452668802722379486185155415065660 u^3 bi8[13,4] = -951.3146379152784513383019821793424939005 u^4 bi8[13,5] = 1769.876627954108227401999032086988914455 u^5 bi8[13,6] = -1814.926158732241586204906382926227921564 u^6 bi8[13,7] = 975.7252379518513874523768974027019911763 u^7 bi8[13,8] = -215.2758042600138267922695001811431333620 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[14] bi8[14,1] = 0. u bi8[14,2] = -78.71890822220322199073537821460790272065 u^2 bi8[14,3] = 702.2030963698086240509004430267820179684 u^3 bi8[14,4] = -2509.783618527791392508610051909561977746 u^4 bi8[14,5] = 4663.884687403353676982783161174879377253 u^5 bi8[14,6] = -4779.049763533834849959594190430001691071 u^6 bi8[14,7] = 2567.969360375736223208476377322945879725 u^7 bi8[14,8] = -566.3684221247208382190594586959862794242 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[15] bi8[15,1] = 0. u bi8[15,2] = -20.19281566680438095870219832836548040387 u^2 bi8[15,3] = 179.3637257949118586258743524266532193814 u^3 bi8[15,4] = -639.8126260732690700781771881696950701907 u^4 bi8[15,5] = 1187.623035597440146280793419574292438396 u^5 bi8[15,6] = -1216.083146478910882267036576696259876826 u^6 bi8[15,7] = 653.1305166034912224190607555907831343139 u^7 bi8[15,8] = -143.9981196370280660478353543467291609746 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[16] bi8[16,1] = 0. u bi8[16,2] = 0. u^2 bi8[16,3] = 0. u^3 bi8[16,4] = 0. u^4 bi8[16,5] = 0. u^5 bi8[16,6] = 0. u^6 bi8[16,7] = 0. u^7 bi8[16,8] = 0. u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[17] bi8[17,1] = 0. u bi8[17,2] = 22.25529172937004228561680254541914022993 u^2 bi8[17,3] = -202.2768882656563899475956661732714767089 u^3 bi8[17,4] = 741.4504035959390672891852702617386096470 u^4 bi8[17,5] = -1420.171375819646417700236265030810075574 u^5 bi8[17,6] = 1506.826759283909640808006726351811877831 u^6 bi8[17,7] = -842.0883145405746016477682230643054253648 u^7 bi8[17,8] = 194.0041240166586589127913551094173499391 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[18] bi8[18,1] = 0. u bi8[18,2] = 14.87763987360506280784259993181818867611 u^2 bi8[18,3] = -312.2840512785346745116969727542541022617 u^3 bi8[18,4] = 1842.506617216153294661664671292748129746 u^4 bi8[18,5] = -4868.899648863078786274115894868122667808 u^5 bi8[18,6] = 6508.346688203267682481628418765155233374 u^6 bi8[18,7] = -4307.866481530869189076138573916573603059 u^7 bi8[18,8] = 1123.319236379456609910815751549228821331 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[19] bi8[19,1] = 0. u bi8[19,2] = 94.98456650525377646383263451778568838647 u^2 bi8[19,3] = -820.5775654295434684704012573738365180124 u^3 bi8[19,4] = 2818.347256898649110692476937532304801453 u^4 bi8[19,5] = -4992.649725157522569698401937223054737557 u^5 bi8[19,6] = 4835.804647435804986125480300928971220935 u^6 bi8[19,7] = -2434.068718877444022356652060555528975267 u^7 bi8[19,8] = 498.1595386248021872436653821733585200624 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[20] bi8[20,1] = 0. u bi8[20,2] = 63.46082596146032232234944838983857033697 u^2 bi8[20,3] = -387.6244695782448432215454472613264482576 u^3 bi8[20,4] = 652.6008727039380999132826268449332985693 u^4 bi8[20,5] = 222.0020976000799700370477743563371275858 u^5 bi8[20,6] = -1696.555363345186459306426642315756771818 u^6 bi8[20,7] = 1674.058335196842891022210000150369785868 u^7 bi8[20,8] = -527.9422985388899807669177601643955622843 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[21] bi8[21,1] = 0. u bi8[21,2] = 57.55994643786018616993511878224123285359 u^2 bi8[21,3] = -588.2803453083489337731949182122044212454 u^3 bi8[21,4] = 2317.048600678134906430718062852747324934 u^4 bi8[21,5] = -4624.295311909926608047251992705773944827 u^5 bi8[21,6] = 5002.133263559409739230532157842265499369 u^6 bi8[21,7] = -2803.532946186995728195816710610623754886 u^7 bi8[21,8] = 639.3667927298664381850782820513480638022 u^8 # #******************************************************** # # FIVE ADDITIONAL STAGES FOR INTERPOLANT OF ORDER 9 # # Coupling coefficients for c[22] = .25e-1 # ---------------------------------------------------- a[22,1] = .1802918623893620731908165792176564180038e-1 a[22,2] = 0. a[22,3] = 0. a[22,4] = 0. a[22,5] = 0. a[22,6] = 0. a[22,7] = 0. a[22,8] = .6983601042028873702545973390560096201728e-1 a[22,9] = -.2541247660791663512384395986842781657182e-1 a[22,10] = .8487827035463274491721441398893680307535e-2 a[22,11] = -.2427525516089801645451101966852425715128e-2 a[22,12] = -.1047839752893819879012607694745789515746 a[22,13] = -.1473147795248041942353840372690095884761e-1 a[22,14] = -.3916338390816177165706892282751065537530e-1 a[22,15] = -.1005657343293959419073236542225421561652e-1 a[22,16] = 0. a[22,17] = .1102510392204834322538452331445716455061e-1 a[22,18] = .5092830749095398308703438556315975226108e-2 a[22,19] = .4759715599420644505591133410826632557391e-1 a[22,20] = .3386307003288382751110965442296681690349e-1 a[22,21] = .2764422831404797700452373965825845732168e-1 # #******************************************************** # # Coupling coefficients for c[23] = .15 # ---------------------------------------------------- a[23,1] = .1677431640522778042988664067637191163626e-1 a[23,2] = 0. a[23,3] = 0. a[23,4] = 0. a[23,5] = 0. a[23,6] = 0. a[23,7] = 0. a[23,8] = .6220437408820475326702539861577894278533 a[23,9] = -.2060859809768841878234097076241307428139 a[23,10] = .1156394989766058889629372195583391792474 a[23,11] = .2664101793378358946544219293685167025971e-1 a[23,12] = -.9376810793418770527505892794460093668860 a[23,13] = -.1367806466702160302637074581619101741312 a[23,14] = -.3678480995268296672182605288991379118419 a[23,15] = -.9547871314402478902820445838193201497337e-1 a[23,16] = 0. a[23,17] = .1013492018422369748729008873270013785313 a[23,18] = -.8911323084568593396468400926074881389560e-1 a[23,19] = .4664140988974760478895528270623735057521 a[23,20] = .4502736292354579812232681662308722738519 a[23,21] = .1838522463326818655346135218242696774099 a[23,22] = 0. # #******************************************************** # # Coupling coefficients for c[24] = .32 # ---------------------------------------------------- a[24,1] = .1071149731491444187554380927165768658192e-1 a[24,2] = 0. a[24,3] = 0. a[24,4] = 0. a[24,5] = 0. a[24,6] = 0. a[24,7] = 0. a[24,8] = -.7094336118221108191937165464264324417735e-1 a[24,9] = .1002164900340091596740582334112699697590 a[24,10] = .1383453980468025108839271214703390659581 a[24,11] = .1796330633578163411338104055485109917477 a[24,12] = .9048246545576180974879274948815422276563e-1 a[24,13] = -.5460662294523338383345981122023862069115e-2 a[24,14] = -.3000457905119619782973021046143166498567e-1 a[24,15] = -.1145192026962799093665613252151017277867e-1 a[24,16] = 0. a[24,17] = .1003394686109385076849515422360600302176e-1 a[24,18] = -.9506485282809046129031027932806241113157e-1 a[24,19] = .4853358804093591445756711642658478691640e-1 a[24,20] = .8013325919783924638483373011297347396327e-1 a[24,21] = -.1251643326835242045676140618774248455713 a[24,22] = 0. a[24,23] = 0. # #******************************************************** # # Coupling coefficients for c[25] = .78 # ---------------------------------------------------- a[25,1] = .1410172088869221367153586187761994182069e-1 a[25,2] = 0. a[25,3] = 0. a[25,4] = 0. a[25,5] = 0. a[25,6] = 0. a[25,7] = 0. a[25,8] = -.3713379753704491105936205420001801316029 a[25,9] = .2231265548117180273161442520179150684520 a[25,10] = .1287005345918120122888629169443916280865 a[25,11] = .2224600659675494761192249831098918110654 a[25,12] = .5382853042550701952740528638168708946100 a[25,13] = .5417202616988763101781128062036252796548e-1 a[25,14] = .1256968791308743925752109039299467082975 a[25,15] = .2784492789002054061504430663197543089132e-1 a[25,16] = 0. a[25,17] = -.3077409246205059733390460511525401688205e-1 a[25,18] = .8569805293689777608077303071761466118035e-2 a[25,19] = -.1535174690587044615794997685221990516897 a[25,20] = -.2179957030548196497189489878038029238243e-1 a[25,21] = .1447128819737186799295514239727801525027e-1 a[25,22] = 0. a[25,23] = 0. a[25,24] = 0. # #******************************************************** # # Coupling coefficients for c[26] = .96 # ---------------------------------------------------- a[26,1] = .1424600411735646609296566581447532773183e-1 a[26,2] = 0. a[26,3] = 0. a[26,4] = 0. a[26,5] = 0. a[26,6] = 0. a[26,7] = 0. a[26,8] = -.3767107393295407091303982522049390741260 a[26,9] = .2252399780730421480874737297000189000070 a[26,10] = .1283603076292529988314451246143633426068 a[26,11] = .2230238705261692544876826347415151339678 a[26,12] = .5463127827750747224899202176094949607118 a[26,13] = .5526190791375779994553849469706124289752e-1 a[26,14] = .1285613508749982456581494397108686240388 a[26,15] = .2857250681296406482698934635829147899039e-1 a[26,16] = 0. a[26,17] = -.2398761886357108720930416967644499057175e-1 a[26,18] = .5556224458910509454379297181908734648749e-1 a[26,19] = -.1740675650762838674257930398070760254668e-1 a[26,20] = -.3815462365996979065575121886854199471011e-1 a[26,21] = .1111878504898917877407531966545730451506e-1 a[26,22] = 0. a[26,23] = 0. a[26,24] = 0. a[26,25] = 0. # # -------------------------------------------------------- # COEFFICIENTS FOR INTERPOLANT bi9 WITH 26 STAGES # -------------------------------------------------------- # # COEFFICIENTS OF bi9[1] bi9[1,1] = 1. u bi9[1,2] = -28.33048870061739823290767301658881994700 u^2 bi9[1,3] = 257.6535452078577977252092979905248156497 u^3 bi9[1,4] = -1152.154455743457311528752964691951881858 u^4 bi9[1,5] = 2909.390878345408890936564599116550031880 u^5 bi9[1,6] = -4355.005172868188498048946108887283528629 u^6 bi9[1,7] = 3834.083497036262189455855371796461857871 u^7 bi9[1,8] = -1835.419052683407081215583427992189311730 u^8 bi9[1,9] = 368.7958613829998340610814211036270246107 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[2] bi9[2,1] = 0. u bi9[2,2] = 0. u^2 bi9[2,3] = 0. u^3 bi9[2,4] = 0. u^4 bi9[2,5] = 0. u^5 bi9[2,6] = 0. u^6 bi9[2,7] = 0. u^7 bi9[2,8] = 0. u^8 bi9[2,9] = 0. u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[3] bi9[3,1] = 0. u bi9[3,2] = 0. u^2 bi9[3,3] = 0. u^3 bi9[3,4] = 0. u^4 bi9[3,5] = 0. u^5 bi9[3,6] = 0. u^6 bi9[3,7] = 0. u^7 bi9[3,8] = 0. u^8 bi9[3,9] = 0. u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[4] bi9[4,1] = 0. u bi9[4,2] = 0. u^2 bi9[4,3] = 0. u^3 bi9[4,4] = 0. u^4 bi9[4,5] = 0. u^5 bi9[4,6] = 0. u^6 bi9[4,7] = 0. u^7 bi9[4,8] = 0. u^8 bi9[4,9] = 0. u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[5] bi9[5,1] = 0. u bi9[5,2] = 0. u^2 bi9[5,3] = 0. u^3 bi9[5,4] = 0. u^4 bi9[5,5] = 0. u^5 bi9[5,6] = 0. u^6 bi9[5,7] = 0. u^7 bi9[5,8] = 0. u^8 bi9[5,9] = 0. u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[6] bi9[6,1] = 0. u bi9[6,2] = 0. u^2 bi9[6,3] = 0. u^3 bi9[6,4] = 0. u^4 bi9[6,5] = 0. u^5 bi9[6,6] = 0. u^6 bi9[6,7] = 0. u^7 bi9[6,8] = 0. u^8 bi9[6,9] = 0. u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[7] bi9[7,1] = 0. u bi9[7,2] = 0. u^2 bi9[7,3] = 0. u^3 bi9[7,4] = 0. u^4 bi9[7,5] = 0. u^5 bi9[7,6] = 0. u^6 bi9[7,7] = 0. u^7 bi9[7,8] = 0. u^8 bi9[7,9] = 0. u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[8] bi9[8,1] = 0. u bi9[8,2] = 2.649656243770091212685381903551424676261 u^2 bi9[8,3] = -96.30312807816005963630382777245983513008 u^3 bi9[8,4] = 869.3095462492795755338599928089438369769 u^4 bi9[8,5] = -3395.688567551074115525201961265641584358 u^5 bi9[8,6] = 6796.933987158715680563278170147156885480 u^6 bi9[8,7] = -7340.848417712071304684606060804637321789 u^7 bi9[8,8] = 4082.848896992365666259441580054990759905 u^8 bi9[8,9] = -919.2934944890586676320942978986329899642 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[9] bi9[9,1] = 0. u bi9[9,2] = -1.563945181928732780647121505551017046606 u^2 bi9[9,3] = 56.84239739272860000194549791973820565214 u^3 bi9[9,4] = -513.1052300304284642178552372517916694426 u^4 bi9[9,5] = 2004.286702110323162741493515173880535381 u^5 bi9[9,6] = -4011.853305913929339500285683507736138334 u^6 bi9[9,7] = 4332.895839278586189971336003691596594090 u^7 bi9[9,8] = -2409.879347937144606091337260195738587773 u^8 bi9[9,9] = 542.6079835318221405169412532400889768401 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[10] bi9[10,1] = 0. u bi9[10,2] = -.8627103334967223830653368770735555216700 u^2 bi9[10,3] = 31.35565375185173442495465167501846267906 u^3 bi9[10,4] = -283.0413682227354209126847112083546012674 u^4 bi9[10,5] = 1105.613463426006937052739159664962261462 u^5 bi9[10,6] = -2213.036200678452629288185991597653042989 u^6 bi9[10,7] = 2390.131097754120588994847482867886207858 u^7 bi9[10,8] = -1329.348266146873716496636094950745123424 u^8 bi9[10,9] = 299.3158071265785138462868993727082901209 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[11] bi9[11,1] = 0. u bi9[11,2] = -1.520295337901214839055193576160469820911 u^2 bi9[11,3] = 55.25592121120227100440616045452813504748 u^3 bi9[11,4] = -498.7844190970740738969945498750124435385 u^4 bi9[11,5] = 1948.346888525776056658403461666308795237 u^5 bi9[11,6] = -3899.882136407551390287649940376076923682 u^6 bi9[11,7] = 4211.964345158858030803618536151121927765 u^7 bi9[11,8] = -2342.619408856117128087568672414857706561 u^8 bi9[11,9] = 527.4637482204278644179968961638568925209 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[12] bi9[12,1] = 0. u bi9[12,2] = -3.846938844125523400516071820264700141179 u^2 bi9[12,3] = 139.8189840986840520353362018994734906611 u^3 bi9[12,4] = -1262.118687621600386514715930156791825893 u^4 bi9[12,5] = 4930.075848057311658057235318456802793199 u^5 bi9[12,6] = -9868.219486069539059368988308801366826185 u^6 bi9[12,7] = 10657.90892434886730229746304583865145121 u^7 bi9[12,8] = -5927.738759872814112912292792695856187255 u^8 bi9[12,9] = 1334.688551172190921099749059976639173619 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[13] bi9[13,1] = 0. u bi9[13,2] = -.3942713061200141454309326713125653612517 u^2 bi9[13,3] = 14.32999476067649707020689155180345562459 u^3 bi9[13,4] = -129.3540665994558117853022852051786116929 u^4 bi9[13,5] = 505.2816077002517600897861155496606850457 u^5 bi9[13,6] = -1011.390080139433268878243655218566636574 u^6 bi9[13,7] = 1092.325051781891697669369143688906543465 u^7 bi9[13,8] = -607.5317019302810290917918493845279272648 u^8 bi9[13,9] = 136.7917244480423273434147193694336909663 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[14] bi9[14,1] = 0. u bi9[14,2] = -.9233145622082101394378429409444333268499 u^2 bi9[14,3] = 33.55834582309798808260613735851232640640 u^3 bi9[14,4] = -302.9246397549735936661321348695774835448 u^4 bi9[14,5] = 1183.281306967867553342903125095128753568 u^5 bi9[14,6] = -2368.498986790111516106072390247333149007 u^6 bi9[14,7] = 2558.034559755808027369106332027405169828 u^7 bi9[14,8] = -1422.733175577880214903071122439856598476 u^8 bi9[14,9] = 320.3423358787481875842587982911148385364 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[15] bi9[15,1] = 0. u bi9[15,2] = -.2068862802930053801253649628830330891017 u^2 bi9[15,3] = 7.519388975651662772174695012120581518594 u^3 bi9[15,4] = -67.87605708082904058354114755731111898667 u^4 bi9[15,5] = 265.1367996984150421661637988925923843021 u^5 bi9[15,6] = -530.7074807559025368587558119659212235622 u^6 bi9[15,7] = 573.1765495641490277116961329189087439579 u^7 bi9[15,8] = -318.7905688834868978004500126002971837241 u^8 bi9[15,9] = 71.77882490212657594681492031347005327988 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[16] bi9[16,1] = 0. u bi9[16,2] = 0. u^2 bi9[16,3] = 0. u^3 bi9[16,4] = 0. u^4 bi9[16,5] = 0. u^5 bi9[16,6] = 0. u^6 bi9[16,7] = 0. u^7 bi9[16,8] = 0. u^8 bi9[16,9] = 0. u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[17] bi9[17,1] = 0. u bi9[17,2] = -.4472441906744099441704338175964823026105 u^2 bi9[17,3] = 16.44684676010503791623763886833381020592 u^3 bi9[17,4] = -154.4086105921295528355180056633078150675 u^4 bi9[17,5] = 641.8986298540248497333509289273669726482 u^5 bi9[17,6] = -1391.939225687982391028602609567895699003 u^6 bi9[17,7] = 1643.890568302952013019278202625162156841 u^7 bi9[17,8] = -1004.065297223317845596795060426393517046 u^8 bi9[17,9] = 248.6243327770222987362193390543305737239 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[18] bi9[18,1] = 0. u bi9[18,2] = -.1507876007899797948720901584434839156279 u^2 bi9[18,3] = 5.527328824824632235316362126620825363280 u^3 bi9[18,4] = -51.33833743084618751433903968701557585387 u^4 bi9[18,5] = 209.6022002703280347991393999433060881829 u^5 bi9[18,6] = -442.7692650421825928714839983614217797969 u^6 bi9[18,7] = 505.0579312588052893780948070449787925777 u^7 bi9[18,8] = -295.6336410615619366143935619944592839974 u^8 bi9[18,9] = 69.70457078142274038253812108643441743987 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[19] bi9[19,1] = 0. u bi9[19,2] = -.6413652207435296452288504944964177537185 u^2 bi9[19,3] = 23.51013248624684600263471193689787394701 u^3 bi9[19,4] = -218.3642683246972281497485359238725613162 u^4 bi9[19,5] = 891.5292818535365634586829868055833114383 u^5 bi9[19,6] = -1883.290177206007885518558760085145850658 u^6 bi9[19,7] = 2148.230954488399755970660772306573864434 u^7 bi9[19,8] = -1257.458401521712336970840850120592935471 u^8 bi9[19,9] = 296.4838434449778148523985255750527153802 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[20] bi9[20,1] = 0. u bi9[20,2] = 1.810729313444845732964058528284532356045 u^2 bi9[20,3] = -66.37479657295337371220255196726289169374 u^3 bi9[20,4] = 616.4952025401106511929691356878863855003 u^4 bi9[20,5] = -2517.003030777322559684753470471663859295 u^5 bi9[20,6] = 5316.984175781033401491488704359579721604 u^6 bi9[20,7] = -6064.976140789574108556866601189158423779 u^7 bi9[20,8] = 3550.109538888391317555902194852386816092 u^8 bi9[20,9] = -837.0456783831301740195014698000522807852 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[21] bi9[21,1] = 0. u bi9[21,2] = .5176008760353717918864555990277480363987e-1 u^2 bi9[21,3] = -1.897337862580348756406065418550014243949 u^3 bi9[21,4] = 17.62264820793629244181715147639285955422 u^4 bi9[21,5] = -71.94907400242465946110661282550878163878 u^5 bi9[21,6] = 151.9871383765666045085018751235590550206 u^6 bi9[21,7] = -173.3686498747860565970136435029707518663 u^7 bi9[21,8] = 101.4806461521468075879782291473158292931 u^8 bi9[21,9] = -23.92713108446217690295957956014097092250 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[22] bi9[22,1] = 0. u bi9[22,2] = 31.32178255668799909977422939838912846070 u^2 bi9[22,3] = -355.6570858339106059687054319211280026146 u^3 bi9[22,4] = 1752.685282489515979253875884672206842255 u^4 bi9[22,5] = -4708.092293138363367969732154806019707156 u^5 bi9[22,6] = 7370.900776193488713149861391844801840850 u^6 bi9[22,7] = -6716.504964764565347011489385051202629762 u^7 bi9[22,8] = 3303.940398161185772296756776169088470785 u^8 bi9[22,9] = -678.5938956640391428503413103061359428182 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[23] bi9[23,1] = 0. u bi9[23,2] = -2.719607334185924760747802644504744092917 u^2 bi9[23,3] = 86.64045615858264001154848875638486632034 u^3 bi9[23,4] = -454.1926030939030807863651114984001402596 u^4 bi9[23,5] = 1014.749221100543425314268817989377200147 u^5 bi9[23,6] = -1133.583456714543865890388885909333783663 u^6 bi9[23,7] = 610.4671827718666569168001429679645990946 u^7 bi9[23,8] = -109.0233499449543802317396567002119357593 u^8 bi9[23,9] = -12.33784294340547057337599296127606178639 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[24] bi9[24,1] = 0. u bi9[24,2] = 3.177214801432923432265738869490200556403 u^2 bi9[24,3] = -113.8098697715142983214434051918276259885 u^3 bi9[24,4] = 978.0935981825675014833003847211971070224 u^4 bi9[24,5] = -3575.129377623670076451027372711378100786 u^5 bi9[24,6] = 6764.361519838450570830405988615992045681 u^6 bi9[24,7] = -6987.161043852012362644872233028628887679 u^7 bi9[24,8] = 3751.905762789571137088934326513342858381 u^8 bi9[24,9] = -821.4378043648253954175634277881875971878 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[25] bi9[25,1] = 0. u bi9[25,2] = .8772843083465530069477626269697233842708 u^2 bi9[25,3] = -31.51810423988375104361582759389916060143 u^3 bi9[25,4] = 273.1229151353221133842213845530391043248 u^4 bi9[25,5] = -993.2198643101781966584366870874238565290 u^5 bi9[25,6] = 1787.888078312663987193988385659681964836 u^6 bi9[25,7] = -1677.394835799640950953367739332661886275 u^7 bi9[25,8] = 781.3579535062687952504707744453846824540 u^8 bi9[25,9] = -141.1134269128985501802080532710905715931 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[26] bi9[26,1] = 0. u bi9[26,2] = 1.719427581798715782378897599231938082126 u^2 bi9[26,3] = -62.89867309250732184389962568482931880335 u^3 bi9[26,4] = 580.3335507873980391019057196688995930872 u^4 bi9[26,5] = -2348.110620506760958600472968113883922730 u^5 bi9[26,6] = 4921.119298612906015908637628774963068611 u^6 bi9[26,7] = -5597.912448707916639109910311016358007839 u^7 bi9[26,8] = 3288.597775149621789973016480733216881572 u^8 bi9[26,9] = -782.8483098245396412116558219612402319811 u^9 # #********************************************************* # Norms of low order INTERPOLANT coefficients on [0,2] # u Max norm 2-norm # ------------------------------------------------- 0.1000000000 -.2984049385e-6 .7396600065e-6 0.2000000000 -.1608224486e-6 .7353601222e-6 0.3000000000 .3410593377e-6 .7287929965e-6 0.4000000000 .1367824727e-6 .3937813579e-6 0.5000000000 .1744614960e-6 .5358967514e-6 0.6000000000 .1844566253e-6 .3735208301e-6 0.7000000000 .3884622065e-6 .4970269218e-6 0.8000000000 .9866067659e-7 .3563409508e-6 0.9000000000 -.4385932639e-6 .7227522131e-6 1.0000000000 .8120949074e-57 .1910890590e-56 1.1000000000 -.5399934977e-5 .9133157010e-5 1.2000000000 -.5125932341e-4 .9337231363e-4 1.3000000000 -.2410449551e-3 .4774423790e-3 1.4000000000 -.8178163556e-3 .1766682915e-2 1.5000000000 -.2275791713e-2 .5359108611e-2 1.6000000000 -.5525304130e-2 .1414961074e-1 1.7000000000 -.1212529087e-1 .3365761501e-1 1.8000000000 -.2459900863e-1 .7374350933e-1 1.9000000000 -.4685019734e-1 .1511170414 2.0000000000 .8900910568e-1 .2928826515 # #********************************************************* # Norms of high order INTERPOLANT coefficients on [0,2] # u Max norm 2-norm # ------------------------------------------------- 0.1000000000 -.1674503122e-7 .5969309359e-7 0.2000000000 -.3154852351e-7 .1098679775e-6 0.3000000000 -.3920097984e-7 .1522367328e-6 0.4000000000 -.3979003422e-7 .1612608602e-6 0.5000000000 -.4217199026e-7 .2457156115e-6 0.6000000000 -.5436032663e-7 .3134685923e-6 0.7000000000 -.5743580598e-7 .3141243295e-6 0.8000000000 .7148385592e-7 .3246402021e-6 0.9000000000 -.6164227589e-7 .3372202613e-6 1.0000000000 -.6336460338e-7 .3490533482e-6 1.1000000000 .2715618776e-6 .1357134866e-5 1.2000000000 .4929707070e-5 .2174780830e-4 1.3000000000 .3505401396e-4 .1528476504e-3 1.4000000000 .1651768762e-3 .7157890654e-3 1.5000000000 .6056436823e-3 .2613144940e-2 1.6000000000 .1867164812e-2 .8029969306e-2 1.7000000000 .5061156739e-2 .2171142563e-1 1.8000000000 .1241173429e-1 .5313829484e-1 1.9000000000 .2808279232e-1 .1200382846 2.0000000000 .5945709726e-1 .2538126022 #*********************************************************`