Initial value problems: finite difference methods, accuracy and stability, heat equation, wave equations, conservation laws and shocks, level sets, Navier-Stokes.
Solving large systems: elimination with reordering, iterative methods, preconditioning, multigrid, Krylov subspaces, conjugate gradients.
Optimization and minimum principles: weighted least squares, constraints, inverse problems, calculus of variations, saddle point problems, linear programming, duality, adjoint methods.
Prerequisites: 18.03 or 18.034
- Time Dependent Problems and Difference Methods
- Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
- Parallel Scientific Computing in C++ and MPI
- Spectral Methods in MATLAB
[01.30.2012] Up-to-date info are avaiable on the stellar course web site. This site is open to MIT only.
[12.19.2011] Course webpages will be updated soon.