% Implict sceme for one-way wave equation

close all; clear all;
global c

c=0.5; 
tfinal = 1;
n = input('n =')
h = 1/n; 

dt = h;  kfinal = fix(tfinal/dt);

for i=1:n+1
  x(i) = (i-1)*h;
  u0(i) = sin(pi*x(i));
end

plot(x,u0); hold

d = 1 + c *dt/h;  alf = - c *dt/h; t=0;

for k=1:kfinal
   t1 = t + dt; 
   u1(1) = uexact(0,t1);          % Boundary condition
   for i=2:n+1,
     u1(i) = (u0(i) + dt*f1(x(i),t1) - alf*u1(i-1) )/d;
   end
   plot(x,u1); pause(0.0)
   u0 = u1; t = t + dt;
end

for i=1:n+1
  err(i) = u1(i)- uexact(x(i),t);
end

  figure(2); plot(x,err)
  format short e
  e2 = [norm(err,1)/n,norm(err,2)/sqrt(n),norm(err,inf)],