- Wednesday, February 3, 2010
- Introduction. Well-posedness of PDEs, and Intro to finite-difference for the heat equation. First notion of
stability.
- Friday, February 5, 2010
- More introduction: sparse linear systems, optimization.
Started IVP: Fourier analysis.
Matlab demo:
heat equation in 1D and
Poisson in 1D
- Monday, February 8, 2010
- IVP for linear PDE, Method of line discretization. ODE stability for the explicit and implicit Euler methods.
- Wednesday, February 10, 2010
- Von Neumann stability analysis
- Friday, February 12, 2010
- Finite-Difference methods for the linear transport equation. Up-wind, down-wind, centered, Lax-Friedrichs,
Lax-Wendroff
- Tuesday, February 16, 2010
- Finished Lax-Wendroff analysis + Matlab demo: Linear transport in 1D. Modified equations.
- Wednesday, February 17, 2010
- Lax equivalence theorem.
- Friday, February 19, 2010
- Error and convergence analysis
- Monday, February 22, 2010
- Convergence plot - matlab demo:
convergenge plot
Advection-diffusion equation.
- Wednesday, February 24, 2010
- 1D linear wave equation.
- Friday, February 26, 2010
- More wave equation. Start Non-linear conservation laws.