Planned schedule is tentative and may be adjusted depending on course progress.
| Lecture | Date | Topics | Handouts | Dues |
|---|---|---|---|---|
| – | Course logistics | Slides | ||
| 1 | Sep 4 | Introduction; finite-difference approximations | Slides | Notes | |
| 2 | Sep 9 | BVPs: boundary value problems, Dirichlet BCs, error, stability | Slides | OA1 (Sep 10) |
| 3 | Sep 11 | BVPs: consistency, convergence, Neumann BCs, nonlinear BVPs | Slides | |
| 4 | Sep 16 | Elliptic PDEs: 2D finite-difference stencils | Slides | OA2 (Sep 17) |
| 5 | Sep 18 | Elliptic PDEs: accuracy, stability | Slides | |
| 6 | Sep 23 | Iterative methods: Jacobi, Gauss–Seidel, descent methods | Slides | Notes | HW1 (Sep 26) |
| 7 | Sep 25 | Iterative methods: conjugate gradient, preconditioning | Slides | Extra | |
| 8 | Sep 30 | Initial value problems: introduction, multistep methods | Slides | Notes | OA3 (Oct 1) |
| 9 | Oct 2 | Initial value problems: convergence, zero-stability | Slides | |
| 10 | Oct 7 | Initial value problems: absolute stability, stiffness | Slides | HW2 (Oct 10) |
| 11 | Oct 9 | Parabolic PDEs: explicit and implicit methods, method of lines | ||
| 12 | Oct 14 | Parabolic PDEs: stability, convergence, multidimensional problems | OA4 (Oct 15) | |
| 13 | Oct 16 | Hyperbolic PDEs: advection equation, characteristics, upwinding | ||
| 14 | Oct 21 | Hyperbolic PDEs: von Neumann stability analysis, CFL condition | HW3 (Oct 24) | |
| 15 | Oct 23 | Hyperbolic PDEs: second-order methods | ||
| 16 | Oct 28 | FVM: finite volume methods, flux, numerical conservation | Final project proposal meeting | |
| 17 | Oct 30 | FVM: Riemann problem, Godunov and Lax–Wendroff method | ||
| 18 | Nov 4 | FVM: high resolution methods, limiters | Final project proposal meeting | |
| 19 | Nov 6 | FVM: nonlinear equations, shocks, ENO methods | ||
| 20 | Nov 11 | Mixed equations: fractional step methods | HW4 (Nov 14) | |
| 21 | Nov 13 | Mixed equations: incompressible Navier–Stokes | ||
| 22 | Nov 18 | Spectral methods: introduction | OA5 (Nov 19) | |
| 23 | Nov 20 | Spectral methods: smoothness, spectral accuracy | ||
| – | Nov 25 | No lecture | ||
| – | Nov 27 | Thanksgiving | ||
| – | Dec 2 | No lecture | HW5 (Dec 5) | |
| 24 | Dec 4 | Spectral methods: Chebyshev spectral methods | ||
| – | Dec 9 | Final project presentations | Final project (Dec 16) | |
| – | Dec 10 | Final project presentations | ||
| – | Dec 11 | Final project presentations |