% This Matlab code solves 1D two-point value problem using SOR(w) method 
%
%    u_xx  = f(x)
% on a square,   0<= x <= 1.
% with Dirichlet BC which is given for u(1), u(n+1).

% function [k,u] = poisson_sor(n,h,w,f,u0,tol)

% u'' - q(x) u = f,   a< x < b, 
% ue = sin (alf x), q(x) = (1+x^2), f(x) = ( - (alf)^2 - (1+x^2) ) sin (alf x)
% Output: k: the number of iterations.
%         u: The computed solution.

clear all; close all

alf = 2; a=0; b=pi;
n = 200; h=(b-a)/n;

tol = 10^(-7); w=1.2;
x=a:h:b;
for i=1:n+1
  f(i) =( - alf*alf - (1+x(i)*x(i)) )* sin (alf* x(i));
  ue(i) = sin (alf* x(i));
  u0(i) = 0;
end

error = 1000; u = u0;

k = 0;
while error > tol
  for i=2:n
     qt = (1+x(i)^2);
     u_temp = (u(i-1) + u(i+1)  ) - h^2*f(i);
     u(i) = (1-w)*u0(i)  + w*u_temp/( 2 + h^2* qt);
  end

  error = max(abs(u-u0));
  u0 = u;
  k = k+1;
end
 
soln_err = max(abs(u-ue)), k