format long;
clear;
fprintf('Solve the nonlinear system by Newton method and SOR method.\n');
fprintf('Use the solution of u with N = 400 as exact solution ue.\n');
u1 = Solve_System(100,1.91);
u2 = Solve_System(200,1.97);
ue = Solve_System(400,1.98);
e1 = 0;
e2 = 0;
for j = 2:100
    for i = 2:100
        e1 = max(e1,abs(ue(4*i-3,4*j-3)-u1(i,j)));
    end
end
for j = 2:200
    for i = 2:200
        e2 = max(e2,abs(ue(2*i-1,2*j-1)-u2(i,j)));
    end
end
p = log2(e2/e1);
fprintf('The error with N = 100 is %.8f.\n',e1);
fprintf('The error with N = 200 is %.8f.\n',e2);
fprintf('The error of the numerical method is O(N^%.0f).\n\n',p);
clear;