% implicit.m - implicit discretisation of the
% heat equation via sparse matrix formulation:
% A*u(new) = u(old)
dx = .025;
x = -1+dx:dx:3-dx;
N = length(x);
dt = input('dt? ');
nu = dt/dx^2;
A = (1+2*nu) * speye(N); for i = 1:N-1
A(i,i+1) = -nu; A(i+1,i) = -nu;
end
u = max([1-abs(x); 0*x])';
x1 = [-1, x, 3];
u1 = [0, u', 0];
while 1
plot(x1,u1,'linewidth',2)
axis([-1 3 0 1]), grid, pause
u = A\u;
x1 = [-1, x, 3];
u1 = [0, u', 0];
end