Refer to the link for more details - https://www.cs.utexas.edu/users/flame/laff/alaff/chapter07-sor.html

https://www.cs.utexas.edu/users/flame/laff/alaff/chapter07-additional-homework.html

Homework 7.5.1.1. In Subsection 7.3.4 we discussed SOR and SSOR. Research how to choose the relaxation parameter w and then modify your implementation of Gauss-Seidel from Homework 7.3.2.1 to investigate the benefits. Homework 7.3.2.1. Modify the code for Homework 7.1.1.1 ( what you now know as the Jacobi iteration) to implement the Gauss-Seidel iteration. Homework 7.1.1.1. The observations in this unit suggest the following way of solving (7,1,1) : - Discretize the domain 011 by creating an (N+2)(N+2) mesh of points. - An (N+2)(N+2) array holds the values u(i,i) plus the boundary around it. - Create an (N+2)(N+2) array F that holds the values f(i,wj) (plus, for convenience, extra values that correspond to the boundary). - Set all values in U to zero. This initializes the last rows and columns to zero, which captures the boundary condition, and initializes the rest of the values at the mesh points to zero. - Repeatedly update all interior points with the formula U(i,j)=(h2f(i,j)F(i,j)+u(i,j1)U(i,j1)+u(i1,j)U(i1,j)+u(i+1,j)U(i+1,j)+u(i,j+1)U(i,j+1))/4 until the values converge. - Bingo! You have written your first iterative solver for a sparse linear system. - Test your solver with the problem where f(,)=(2+2)2sin()sin(). - Hint: if x and y are arrays with the vectors x and y (with entries i and j), then mesh (x,y,U) plots the values in U. - Hint -Solution in-contoxt - Solution Assignments/Week07/answers/Poisson_G5_iteration.m. When you execute the script, in the COMMAND WINDOW enter "RETURN" to advance to the next iteration. You may also want to observe the Jacobi and Gauss-Seidel iterations in action side-by-side in Assignments/Weck07/answers/Poisson_acobi_vs_GS.m