Write a function x = poisson1dj(f, n, numiter) that uses the Jacobi iterations to numerically approximate the solution to the one-dimensional Poisson equation 20.26, where is the right-hand side, is...

Write a function x = poisson1dj(f, n, numiter) that uses the Jacobi iterations to numerically approximate the solution to the one-dimensional Poisson equation 20.26, where

is the right-hand side,

is the number of subintervals of

and numiter is the number of iterations.

Do part

using the Gauss-Seidel iteration by writing a function poisson1dgs. If you have done Problem

use red-black ordering.

The exact solution to the Poisson equation

Using
and numiter

(Jacobi), numiter

compute the solution using poisson1dj and poisson1dgs. Compare the results to the true solution.