| 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 |