| Date |
Topics |
| Aug 7, 2025 |
Solving equations of motion: finite difference (FD) method, Euler method |
| Aug 14, 2025 |
Solving equations of motion: implicit Euler method, symplectic Euler method, Heun method, Runge-Kutta methods |
| Aug 21, 2025 |
Solving Laplace and Poisson equations using the FD method, iterative methods for solving a sparse linear system of algebraic equations |
| Aug 28, 2025 |
Solving the heat/diffusion equation using the FD method: implicit and explicit schemes, von Neuman stability analysis |
| Sep 4, 2025 |
Solving the wave equation in unbounded domains using the FD method |
| Sep 11, 2025 |
Solving the acoustic/elastic wave equations and Maxwell's equations using the FD method |
| Sep 18, 2025 |
Solving the Helmholtz equation using the FD method |
| Sep 25, 2025 |
Solving the time-dependent Schrodinger equation using the FD method |
| Oct 9, 2025 |
Solving the time-independent Schrodinger equation using the Numerov method |
| Oct 16, 2025 |
Solving the eikonal equation using the upwind FD method |
| Oct 30, 2025 |
Solving the diffusion-advection equation using the FD method: a splitting approach for mixed-type PDE |
| Nov 6, 2025 |
Solving PDEs in other coordinate systems |
| Nov 13, 2025 |
Higher-order FD method and spectral method |
| Nov 20, 2025 |
Solving PDEs in complex domains using the finite-element (FE) method |
| Nov 27, 2025 |
Solving PDEs in complex domains using the finite-element (FE) method (continued) |
| Dec 18, 2025 |
Project presentation |