n=20;
h=1/20;

% Define the tridiagonal matrix A
D = sparse(1:n,1:n,-2*ones(1,n),n,n);
E = sparse(2:n,1:n-1,ones(1,n-1),n,n);
A = E+D+E';
A(1,1)=-1;

% Define the right-hand side b1
x=[0:h:1-h];
b=h^2*exp(x);
b1=b;
b1(1)=0;

% Solve for u where Au=b1
u1=b1/A;

% Try a different right-hand side b2
b2=b;
b2(1)=h^2/2*exp(x(1));

% Solve for u in Au=b2
u2=b2/A;

% Compute the exact solution
uexact=exp(x)-x+1-exp(1);

% Plot the exact solution with the computed solution
figure(1)
clf
plot(x,uexact)
axis([0 1 -0.8 0])
hold on
plot(x,u1,'+')
plot(x,u2,'o')
hold off
myh=legend('Exact solution ','Solution with 1-sided at bdy', ...
'Solution with centered at bdy',0);
xlabel('x')
ylabel('u')
Ha_ax=gca;set(Ha_ax,'Fontsize',12);