Matlab code: Implement Jacobi's iteration method to nd an approximation of the solution of

 

 

Homework 1 Instructor: Prof. Hector D. Ceniceros
General Instructions: Please write your homework papers neatly. You need to turn in
both full printouts of your codes and the appropriate runs you made. Write your own code,
individually. Do not copy codes!
1. Consider the linear system of the boundary value problem of homework # 4, i.e.
−vj−1 + 2vj − vj+1
+ π 2 vj = 2π 2 sin(πxj ) for j = 1, 2, . . . , N − 1.
2
h (1) .
(a) Implement Jacobi’s iteration method to find an approximation of the solution of
(1) using a stopping criterium of kb − Ax(k) k2 /kbk2 < 0.1h, with h = 1/N . Do
this for N = 50 and N = 100 and comment on the required number of iterations.
(b) Repeat (a) for the Gauss-Seidel iteration.
(c) Repeat (b) for the Conjugate Gradient Method and compare the performance
with that of the Jacobi and Gauss-Seidel iterations. 1 All course materials (class lectures and discussions, handouts, homework assignments, examinations, web
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materials without the prior written permission of the instructor. 1

Attachments:

• 1492593238-homework_5Ns.pdf