Course: CAAM 31100 =STAT 31100, MATH 38309,CMSC 37812
Title: Mathematical Computation III: Numerical Methods for PDE's
Instructor(s): Yuehaw Khoo
Teaching Assistant(s): Yuming Chen
Class Schedule: Sec 01: TuTh 11:00 AM–12:20 PM in Jones 226
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.