MATLAB® software is required to run the .m files in this section.
The lecture notes are available as a single (PDF) file, or as separate files related to the lectures in the table below.
Lecture Notes Table
| LEC # |
TOPICS |
NUMERICAL EXAMPLES AND HANDOUTS |
| 1 |
Introduction, Examples |
|
| 2 |
Linear Systems |
|
| 3 |
The Fast Fourier Transform (PDF) |
|
| 4 |
Wave Equation (PDF) |
Supplemental Handout (PDF) |
| 5 |
Consistency, Stability, Convergence, Von Neumann Analysis (PDF) |
|
| 6 |
Conditions for Stability (PDF) |
|
| 7 |
Multistep Schemes
Leap-frog (PDF) |
|
| 8 |
Dissipation (PDF) |
Numerical Example (M) |
| 9 |
Dispersion (PDF) |
|
| 10 |
Group Velocity and Propagation of Wave Packets I (PDF) |
Numerical Example (M) |
| 11 |
Group Velocity and Propagation of Wave Packets II (PDF) |
|
| 12 |
Parabolic Equations (PDF) |
Supplemental Handout (PDF) |
| 13 |
The Du Fort Frankel Scheme (PDF) |
Numerical Example (M) |
| 14 |
The Convection-Diffusion Equation (PDF) |
Numerical Example (M) |
| 15 |
Systems of Differential Equations (PDF) |
|
| 16 |
The Solution of the System ut + Aux = Bu (PDF) |
|
| 17 |
The Solution of the System ut + Aux = Buy (PDF) |
|
| 18 |
ADI Methods (PDF) |
|
| 19 |
Elliptic Equation (PDF) |
|
| 20 |
Numerical Methods for Elliptic Equations (PDF) |
|
| 21 |
Detailed Analysis of Jacobi, Gauss-Seidel and SOR(w) (PDF) |
|
| 22 |
Multigrid, Part I |
Numerical Example Mgdemo.m and others located here |
| 23 |
Multigrid, Part II |
|
| 24 |
Numerical Methods for ODEs (PDF) |
Numerical Example (M) |
| 25 |
Stiff ODEs (PDF) |
|