SCHEDULE
Note: The schedule is subject to change. Check back for changes and updates
| Date | Topic | Reading |
|---|---|---|
| Jan 10 Tue | Introduction; Finite Difference Approximation | Textbook |
| Jan 12 Th | Finite Difference Schemes for the Poisson's Equation | Lecutre Notes |
| Jan 17 Tue | 2D Poisson's Equation | Lecutre Notes |
| Jan 19 Th | 2D Poisson's Equation; well-posedness | Lecutre Notes |
| Jan 24 Tue | Fourier analysis; well-posedness | Lecutre Notes |
| Jan 26 Th | well-posedness | Lecutre Notes |
| Jan 31 Tue | ODE, basic numerical methods, consisitency, 0-stability | Lecutre Notes |
| Feb 2 Th | Absolute stability, stability region | Lecutre Notes |
| Feb 7 Tue | Runge-Kutta. | Lecture notes and textbook |
| Feb 9 Th | Multistep methods. | Lecture notes and textbook; Use the code on blackboard to plot the stability region. |
| Feb 14 Tue | Stability for LMM. | Lecture notes and textbook. |
| Feb 16 Th | Basic concepts of finite difference methods | Lecutre Notes 5.1 |
| Feb 21 Tue | Lax Equivalence Theorem | Lecutre Notes 5.2 |
| Feb 23 Th | Well posedness for constant coefficient problems; Hyperbolic equations | Lecutre Notes 3.3 |
| Feb 28 Tue | No Class. Out of Town. | |
| Mar 2 Th | Well posedness for hyperbolic equations | Lecutre Notes3.4 |
| Mar 7 Tue | Stability for constant coefficient FD schemes | Lecutre Notes |
| Mar 9 Th |
Stability of the leapfrog scheme |
Lecutre Notes |
| Mar 14 Tue | No Class. Spring Vacation. | |
| Mar 16 Th | No Class. Spring Vacation. | |
| Mar 21 Tue | Stability of the leapfrog scheme | Lecutre Notes |
| Mar 23 Th | Dissipative schemes | Lecutre Notes |
| Mar 28 Tue | Iterative methods: Jacobi, GS, SOR | Lecutre Notes |
| Mar 30 Th | Steepest Descent and Conjugate Gradient | Lecutre Notes |
| Apr 4 Tue | Multigrid methods | Lecture notes and 6.9 in Applied Numerical Linear Algebra* |
| Apr 6 Th | Multigrid methods | |
| Apr 11 Tue | Upwind schemes for 1D hyperbolic systems | Lecutre Notes |
| Apr 13 Th | Solutions of HW3 | |
| Apr 18 Tue | Lax-Wendroff schemes for 1D hyperbolic systems | Lecutre Notes |
| Apr 20 Th | Boundary conditions for 1D hyperboic problems | Lecutre Notes |
| Apr 25 Tue |
Kreiss theory, well posedness of boundary conditions |
Lecutre Notes |
| Apr 27 Tue |
Kreiss theory, well posedness of boundary conditions | Lecutre Notes |
