what is the problem with this code gauss siedel . Only processing one solution but it should be twenty solutions

Question

Sarvjeet Singh 2021-4-10

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/798202-what-is-the-problem-with-this-code-gauss-siedel-only-processing-one-solution-but-it-should-be-twen

编辑： Cris LaPierre 2021-4-10

clc
clear all
area=0.01; % Cross sectional area (m^2)
l=1; % Length of the rod (m)
k=5; % Thermal conductivity (W/mK)
g=20000; % Heat generation (W/m^3)
T1=100; % Temperature at one end (At x=0) 
T2=500; % Temperature at the other end (At x=1m)
delta_x=0.05; % Cell spacing
n=20; % Number of cells
s= (k*area)/delta_x;
% Formulate the matrix form Ax=B
% Define matrix A
A=zeros(n,n);
A(1,1)= 3*((k*area)/delta_x);
A(20,20)=A(1,1);
A(2,1)= -((k*area)/delta_x);
A(20,19)=A(2,1);
% Define matrix B
B(1)=g*area*delta_x+2*s*T1;
B(2:19)=g*area*delta_x;
B(20)=g*area*delta_x+2*s*T2;
% For solution matrix x
x(1:n)=150; % Initial guess is taken as 150 at all nodes
normVal=Inf; 
tol=1e-3; GaussItr=0;
plotGauss=[];
while normVal>tol
    x_old=x;
    
    for i=1:n
        
        sigma=0;
        
        for j=1:i-1
                sigma=sigma+A(i,j)*x(j);
        end
        
        for j=i+1:n
                sigma=sigma+A(i,j)*x_old(j);
        end
        
        x(i)=(1/A(i,i))*(B(i)-sigma);
    end
    
    GaussItr=GaussItr+1;
    normVal=norm(x_old-x);
    plotGauss=[plotGauss;normVal];
end
fprintf('Solution of the system is : \n%f\n%f\n%f\n%f\n%f in %d iterations',x,GaussItr);