solve discrete poisson equation using sor in matlab

main.m
% Parameters
N = 100;                % Number of grid points
L = 1.0;                % Length of the domain
dx = L / (N - 1);       % Grid spacing
omega = 1.8;            % Relaxation parameter
tolerance = 1e-6;       % Convergence tolerance
maxIterations = 1000;   % Maximum number of iterations

% Define the grid
x = linspace(0, L, N)';
y = linspace(0, L, N)';
[X, Y] = meshgrid(x, y);

% Set up the initial solution grid
phi = zeros(N, N);

% Set up the boundary conditions
phi(:, 1) = 1.0;    % Left boundary
phi(:, end) = 0.0;  % Right boundary
phi(1, :) = 0.0;    % Bottom boundary
phi(end, :) = 0.0;  % Top boundary

% Solve the Poisson equation using the SOR method
iterations = 0;
delta = tolerance + 1;
while delta > tolerance && iterations < maxIterations
    previousPhi = phi;
    for i = 2:N-1
        for j = 2:N-1
            phi(i, j) = (1 - omega) * phi(i, j) + (omega / (4 + dx^2)) * (phi(i+1, j) + phi(i-1, j) + phi(i, j+1) + phi(i, j-1));
        end
    end
    delta = max(abs(phi(:) - previousPhi(:)));  % Calculate the maximum change
    iterations = iterations + 1;
end

% Display the solution
figure;
imagesc(x, y, phi');
axis equal tight;
colorbar;
xlabel('x');
ylabel('y');
title('Solution of the Poisson Equation using SOR');
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