Gauss-Seidal solver for 1D heat equation
1 vue (au cours des 30 derniers jours)
Afficher commentaires plus anciens
I tried using Gauss-Seidal solver by computing A and the right hand side. But still got an error:) asking for help.
x_min= 0;
x_max = 1;
N = 10;
lamda=15;
L = x_max-x_min;
h = L/N;
x = linspace(x_min,x_max,N+1)';
uexact= @(x) 8*(x-3*x.^2+4*x.^3-2*x.^4);
% uexact= @(x) 4*(x-x.^2);
% f = @(x) 8*lamda*ones(1,N-1); % Source term
f = @(x) 48*lamda*(2*x-1).^2;
u_exact = uexact(x);
ua = uexact(x_min);
ub = uexact(x_max);
u = zeros(N-1,1);
A = zeros(N-1,N-1);
b = f(x(2:N)); %
b(1) = b(1) + ua/h^2;
for i=2:N-1
b(i) = b(i) + ub/h^2;
end
A1 = diag( 2*ones(1,N-1) );
A2 = diag( -1*ones(1,N-2), 1 );
A3 = diag( -1*ones(1,N-2), -1 );
A = (A1 + A2 + A3);
A = lamda*A/h^2;
x0=zeros(N-1,1);
tol=0.0001;
M=1000000;
k=1;
x2=x0;
while(k<M)
n = length(b);
x2(1)=(b(1)-A(1,2)*x0(2)-A(1,3)*x0(3))/A(1,1);
for j = 2 : n
x2(j)=(b(j)-A(j,1:j-1).*x2(1:j-1)-A(j,j+1:n).*x0(j+1:n))./A(j,j);
end
x1=x2';
error=abs(x1(j))-x0;
if norm(error)< tol%if norm(x1-x0)< tol
disp('succefful');
break
end
end
plot(x,x1)
5 commentaires
Réponses (0)
Voir également
Catégories
En savoir plus sur Matrix Indexing dans Help Center et File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!