Numerical Analysis of
Time-Dependent Problems

The main topic is finite difference methods for time-dependent differential equations.

• Review of numerical methods for ODEs (initial value problems)
  • Consistency, convergence
  • Zero stability and absolute stability, stability regions
  • Linear multistep and Runge-Kutta methods
  • Stiff problems, BDF methods
  • Software

• Numerical Methods for time-dependent partial differential equations
  • Hyperbolic and parabolic equations
  • Explicit and implicit methods
  • Lax-Richtmyer stability, von Neumann analysis
  • Method of lines approach, relation to stiff ODEs
  • Finite volume methods
  • Introduction to shock capturing methods, flux limiters
  • Spectral and pseudospectral methods
  • Convection-diffusion and reaction-diffusion equations

Prerequisites: Familiarity with partial differential equations and Matlab. Amath 581 or Amath 584 strongly recommended.

See the webpage for more information: