PPAGAF GS

HGCGC

% Gauss Seidel Method.
format long 
x = [0.1; 0.1; -0.1]; % INITIAL GUESS.
i = 0;                % INITIAL ITERATION COUNT.

while i <= 100
    x_old = x; % Store the previous iteration values
    
    % Update the recent values
    x(1) = (1/3)*(cos(x(2)*x(3)) + 0.5);          
    x(2) = (1/9)*(sqrt(x(1)^2 + sin(x(3)) + 1.06)) - 0.1;
    x(3) = (1/20)*((3 - 10*pi)/3 - exp(-x(1)*x(2)));

    % Compute the error percentage for each element
    error_percentage = abs(x - x_old) ./ abs(x_old) * 100;
    
    % Check difference
    if max(abs(x - x_old)) < 0.00000000001
        break;
    end
    
    disp('i = ')
    disp(i)
    disp("X = ")
    disp(x)
    disp("Error Percentage = ")
    disp(error_percentage)
    
    
    i = i + 1; % INCREASING THE ITERATION COUNT.
end 


% Plotting
figure;
plot(0:i, x(1), '-o', 0:i, x(2), '-o', 0:i, x(3), '-o');
xlabel('Iteration');
ylabel('Value');
title('Variation of x(1), x(2), and x(3) over Iterations');
legend('x(1)', 'x(2)', 'x(3)', 'Location', 'best');
grid on;