Heat Equation 1D Finite Difference solution

% Heat equation in 1D
% The PDE for 1D heat equation is Ut=Uxx, 0=<t,0=<x=<L
% Initial condions are U(0,t)=a(t);U(L,t)=b(t)
% the boundary condition is U(x,0)=g(x)
% u(t,x) is the solution matrix.
% the finite linear heat equation is solved is....
% -u(i-1,j)=alpha*u(i,j-1)-[1+2*alpha]*u(i,j)+alpha*u(i,j+1)...(1)
%alpha=dx/dt^2. dx,dt are finite division for x and t.
% t is columnwise
%x is rowwise dealt in this code
%suggestions and discussions are welcome.