Question

5. (20 points) Prepare the necessary equations by hand and create a matlab script that solves the follo- wing non-linear BVP. Use n-10 and keep the number of iterations at 20.

Answer 1

Matlab code

lo lo 3 limen

clc
clear all
n=10;
h=1/n;
x=0:h:0.9;
x=x'
A=full(gallery('tridiag',n,-1,2,-1))
v=zeros(n,1);
for k=1:20
v=-h.^2*inv(A)*(3*v+x.^2+10*v.^3);
end
%end
v

Output

x =

0
0.1000
0.2000
0.3000
0.4000
0.5000
0.6000
0.7000
0.8000
0.9000

A =

2 -1 0 0 0 0 0 0 0 0
-1 2 -1 0 0 0 0 0 0 0
0 -1 2 -1 0 0 0 0 0 0
0 0 -1 2 -1 0 0 0 0 0
0 0 0 -1 2 -1 0 0 0 0
0 0 0 0 -1 2 -1 0 0 0
0 0 0 0 0 -1 2 -1 0 0
0 0 0 0 0 0 -1 2 -1 0
0 0 0 0 0 0 0 -1 2 -1
0 0 0 0 0 0 0 0 -1 2

v =

-0.0048
-0.0098
-0.0149
-0.0201
-0.0250
-0.0291
-0.0315
-0.0313
-0.0271
-0.0173