COURSE DESCRIPTION
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 and 18.034
Text Book: Gilbert Strang, Computational Science and Engineering, Wellesley-Cambridge Press, 2007
Reference Books:
- Time Dependent Problems and Difference Methods
- Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
- Applied Numerical Linear Algebra
- Numerical Methods for Conservation Laws by R. J. LeVeque
- Iterative Methods for Sparse Linear Systems
- Spectral Methods in MATLAB
- Convex Optimization
RECENT UPDATE
Pset 4 is posted. Due on April 29th.
Read 6.9 in Applied Numerical Linear Algebra for multigrid method.
Pset 3 is posted. Due on April 8th.
Read LeVeque's book or lecture notes in 16.920 for nonlinear conservation laws.
Pset 2 is posted. Due on Mar. 13th.
Pset 1 is posted. Due on Feb. 27th.
Read lecture notes of 18.330 regarding Fourier Transform.
