Midterm Review

1. Classification of PDEs into parabolic, hyperbolic and elliptic type.
2. A hand calculation using the 5-point formula for solving the Poisson equation on a very coarse grid.
3. Explanation of the upwind difference method for solving a general linear elliptic problem and when to use it.
4. Definition of the shift, forward difference, backwards difference, central difference and averaging operators.
5. Proof of the Gershgorin circle criterion.
6. Statement of Lemma 10.1 in Iserles on the convergence of the one-step stationary scheme x=Hx+v to a solution of Ax=b.
7. Description and comparison of the Jacobi, Gauss-Seidel and SOR iterative methods.
8. Definitions of spectral radius, positive definite and diagonally dominant.
9. Explanation of multigrid and intuitively what is needed for it to work.