solution:

function [y]=pdeeq()

format long;
h=0.1;
k=0.005;
l=k/(h^2);

x=0:h:1;
t=0:k:0.015;

for i=1:length(x)
u(i,1)=sin(pi*x(i));
end
for i=1:length(t)
u(1,i)=0;
u(length(x),i)=0;
end

for j=1:length(t)-1
for i=2:length(x)-1
u(i,j+1)=l*(u(i+1,j)+u(i-1,j))+(1-2*l)*u(i,j);
end
end

disp(u);

Solution:

    

             t=0                             t=0.005                  t=0.010                t=0.015

                0                   0                   0                   0
   0.309016994374947   0.293892626146237   0.279508497187474   0.265828377610012
   0.587785252292473   0.559016994374947   0.531656755220025   0.505635621484342
   0.809016994374947   0.769420884293813   0.731762745781211   0.695947727757254
   0.951056516295154   0.904508497187474   0.860238700294483   0.818135621484342
   1.000000000000000   0.951056516295154   0.904508497187474   0.860238700294484
   0.951056516295154   0.904508497187474   0.860238700294484   0.818135621484342
   0.809016994374947   0.769420884293814   0.731762745781211   0.695947727757254
   0.587785252292473   0.559016994374947   0.531656755220025   0.505635621484342
   0.309016994374948   0.293892626146237   0.279508497187474   0.265828377610013
                   0                   0                   0                   0