Week # Topics
Initial Value Problems
1 Differential Equations and Stable Difference Methods
2 Finite Differences: Accuracy, Stability, Convergence
3 The Wave Equation and von Neumann Stability
4 The Heat Equation and Convection-Diffusion
5 Maxwell's Equations and Staggered Leapfrog
6 Nonlinear Flow Equations
7 Separation of Variables and Spectral Methods
Solving Large Linear Systems
8 Elimination with Reordering
9 Iterative Methods
10 Multigrid Methods
11 Krylov Methods
12 Saddle Points and the Stokes Problem
13 Optimization
Project Reports