| LEC # | TOPICS | KEY DATES |
|---|---|---|
| 1 | Introduction, Examples | |
| 2 | Linear Systems | |
| 3 | The Fast Fourier Transform | |
| 4 | Wave Equation | |
| 5 | Consistency, Stability, Convergence, Von Neumann Analysis | |
| 6 | Conditions for Stability | Homework 1 due |
| 7 | Multistep Schemes Leap-frog | |
| 8 | Dissipation | |
| 9 | Dispersion | |
| 10 | Group Velocity and Propagation of Wave Packets I | Homework 2 due |
| 11 | Group Velocity and Propagation of Wave Packets II | |
| 12 | Parabolic Equations | |
| 13 | The Du Fort Frankel Scheme | |
| 14 | The Convection-Diffusion Equation | Homework 3 due |
| 15 | Systems of Differential Equations | |
| 16 | The Solution of the System ut + Aux = Bu | |
| 17 | The Solution of the System ut + Aux = Buy | |
| 18 | ADI Methods | Homework 4 due |
| 19 | Elliptic Equation | Homework 5 due |
| 20 | Numerical Methods for Elliptic Equations | |
| 21 | Detailed Analysis of Jacobi, Gauss-Seidel and SOR(w) | |
| 22 | Multigrid, Part I | |
| 23 | Multigrid, Part II | |
| 24 | Numerical Methods for ODEs | |
| 25 | Stiff ODEs | Homework 6 due |