COURSE DESCRIPTION
Syllabus
LECTURE NOTES (updated on April 18)Mathworks online courses for learning MATLAB
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 Jan 30 (extended to Feb 9) Poisson1D_Dirichlet.m Poisson2D_Neumann.mHOMEWORK # 2 due on Feb 23 (extended to Mar 5) Kepler_reference_q.mat
Demo code to draw ODE solver stability region
HOMEWORK # 3 due on Mar 19
HOMEWORK # 4 due on April 9
Schedule
Note: The schedule is subject to change. Check back for changes and updates
| Date | Topic |
|---|---|
| Week 1 (Jan 9 11) |
Introduction. Finite Difference for Poisson Equation. |
| Week 2 (Jan 16 18) | Fourier Transform and Fourier Series. |
| Week 3 (Jan 23 25) | Chapter 2: 2D Poisson Equation and Neumann b.c. |
| Week 4 (Jan 30 Feb 1) | Section 5.1 Wellposedness; Chapter 6 ODE: Section
6.1-6.8 |
| Week 5 (Feb 6 8) | Runge-Kutta method; Chapter 7 Finite Difference Scheme
for time-dependent PDEs |
| Week 6 (Feb 13 15) | Chapter 7 stability; von Neumann
stability |
| Week 7 (Feb 20 22) | Stability of leapfrog and upwind schemes for wave
equations; Wellposedness of systems |
| Week 8 (Feb 27 29) | Wellposeness of hyperbolic equations;
finite element method Chapter 3 |
| Week 9 (Mar 5 7) | Chapter 3: finite element method |
| Week 10 (Mar 12 14) | Spring Break: No Class |
| Week 11 (Mar 19 21) | Finite element method; introduction to conservation
laws |
| Week 12 (Mar 26 28) | Finite element method: purely Neumann b.c. and
nonhomogeneous Dirichlet b.c. |
| Week 13 (April 2 4) | Concluding remarks on FEM; conservation laws |
| Week 14 (April 9 11) | conservation laws |
| Week 15 (April 16 18) | Poisson equation in TV minimization; conservation laws |
| Week 16 (April 23 25) | Notes
on conservation laws |
| Week 17 (April 30 May 2) | Final Exam Week: No Class |
