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Problem 1:

T=1;
n=100;m=10;
dt=T/n;
xmin=-1; xmax=1;
dx=2/m;
t=0:dt:T; x=-1:dx:1;
U=zeros(m+1,n+1);
U(:,1)=2*x'+1;
U(1,:)=-ones(n+1,1);
U(m+1,:)=3*ones(n+1,1);
alpha=dt/dx^2;
% d1=diag(ones(1,m-1));d2=diag(ones(1,m-2),1)...
%    +diag(ones(1,m-2),-1);
% A=(1+alpha)*d1-0.5*alpha*d2;
% B=(1-alpha)*d1+0.5*alpha*d2;
A=(1+alpha)*diag(ones(1,m-1))-0.5*alpha*diag(ones(1,m-2),1)...
    -0.5*alpha*diag(ones(1,m-2),-1);
B=0.5*alpha*(-2*diag(ones(1,m-1))+diag(ones(1,m-2),1)...
    +diag(ones(1,m-2),-1));
inv(A)
for k=1:n...

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