Recommended Text: BURDEN AND FAIRES, Numerical Analysis. Nelson, 7th edition.

• ODEs - Initial Value Problems
  • Runge Kutta methods
  • Stability
  • ODEs, Euler's method, Taylor methods (review)
  • Linear Multistep Methods
  • Predictor-corrector methods
  • Systems of ODEs

• ODEs - Two point boundary value problems
  • Initial value methods (shooting)
  • Finite Differences
  • Ritz methods and collocation methods

• Fourier Analysis
  • Fourier transform
  • Discrete Fourier transform

• Time-dependent PDEs
  • Finite difference formulae
  • Method of lines
  • Finite differences and Fourier analysis

• Accuracy, stability and convergence
  • Lax Equivalence
  • The CFL condition
  • The von Neumann condition

• Spectral Methods
  • Periodic boundary conditions
  • Polynomial spectral methods

• Elliptic PDEs
  • Laplace equation
  • Finite Differences
  • Iterative Methods
  • Multigrid Methods

Please read how the Assignment Lab accounts work