Course: STAT 31100=CAAM 31100, CMSC 37812, MATH 38309
Title: Mathematical Computation III: Numerical Methods for PDE's
Instructor: Siyao Yang
Class Schedule: Sec 1: TR 2:00 PM–3:20 PM in TBA
Description: The first part of this course introduces basic properties of PDE's; finite difference discretizations; and stability, consistency, convergence, and Lax's equivalence theorem. We also cover examples of finite difference schemes; simple stability analysis; convergence analysis and order of accuracy; consistency analysis and errors (i.e., dissipative and dispersive errors); and unconditional stability and implicit schemes. The second part of this course includes solution of stiff systems in 1, 2, and 3D; direct vs. iterative methods (i.e., banded and sparse LU factorizations); and Jacobi, Gauss-Seidel, multigrid, conjugate gradient, and GMRES iterations.