In Chapter 12, we used finite difference methods to approximate the solution of the heat equation in one spacial variable. We needed to solve a tridiagonal linear system with coefficient matrix This...

In Chapter 12, we used finite difference methods to approximate the solution of the heat equation in one spacial variable. We needed to solve a tridiagonal linear system with coefficient matrix

This matrix is strictly row diagonally dominant, and so both the Jacobi and Gauss-Seidel iterations will converge.

 Let
and solve the
 linear system
 with

^T
using the Jacobi iteration with tol

⁻¹⁴
 numiter
 and

₀

 Do part
 using the Gauss-Seidel iteration.

 Do part
 using SOR with
 Which value of ω works best

 Solve the system using the MATLAB function thomas introduced in Section

 Solve the system using the MATLAB command “B\c.”

 Compare the results of parts