COURSE DESCRIPTION
Syllabus
LECTURE NOTES (updated on Mar 24)Reference Books (for those with *, online access available via Purdue Library):
- Randall J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, Steady State and Time Dependent Problems*
- Randall J. LeVeque, Numerical Methods for Conservation
Laws*
- John C. Strikwerda, Finite Difference Schemes and Partial Differential Equations*
- G. Strang, Computational Science and Engineering
- Trefethen and David Bau, Numerical Linear Algebra
- Gustafsson, Bertil; Kreiss, Heinz-Otto; Oliger, Joseph, Time Dependent Problems and Difference Methods
- U. M. Ascher; Linda Ruth Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
- Demmel, James W., Applied Numerical Linear Algebra*
- Y. Saad, Iterative Methods for Sparse Linear Systems*
- Lloyd N. Trefethen, Spectral Methods in MATLAB*
Problem Sets (Solutions will be posted on Brightspace)
HOMEWORK # 1 due on Feb 8 Poisson1D_Dirichlet.m Poisson2D_Neumann.mHOMEWORK#2 due on Feb 22 Kepler_reference_q.mat
Demo code to draw ODE solver stability region
HOMEWORK#3 due on Mar 10 (extended to Mar 22)
HOMEWORK#4 due on April 5
HOMEWORK#5 due on April 19 Poisson2D_Dirichlet.m
Schedule
Note: The schedule is subject to change. Check back for changes and updates
| Date | Topic |
|---|---|
| Week 1 (Jan 11 13) |
Introduction. Finite Difference for Poisson Equation. |
| Week 2 (Jan 18 20) | Finite Difference, 2D Discrete Laplacian |
| Week 3 (Feb 1 3) | Fourier Series. Well-posedness. |
| Week 4 (Feb 8 10) | ODE, Runge Kutta, stability region. |
| Week 5 (Feb 15 17) | PDE: von Neumann stability |
| Week 6 (Feb 22 24) | von Neumann stability; wellposedness for hyperbolic problems |
| Week 7 (Mar 1 3) | hyperbolic problems; Finite Element Method |
| Week 8 (Mar 8 10) | Finite Element Method |
| Week 9 (Mar 15 17) | Spring Break: No Class |
| Week 10 (Mar 22 24) | Finite Element Method |
| Week 11 (Mar 29 31) | linear solvers |
| Week 12 (April 5 7) | Conjugate gradient; nonlinear conservation laws |
| Week 13 (April 12 14) | nonlinear conservation laws |
| Week 14 (April 19 21) | nonlinear conservation laws |
| Week 15 (April 26 28) | Optimization perspectives |
| Week 16 (May 3 5) | Final Exam |
