my code wont display figure

% Parameters
L = 1; % Length of the string
c = 1; % Wave speed
num_segments = 200; % Number of segments
dx = L / num_segments; % Discretization step
dt = 0.005; % Time step
num_steps = 10 / dt; % Number of time steps
% Initial wave parameters
left_wave_length = 0.15 * L;
right_wave_length = 0.25 * L;
% Initialize the wave function
x = 0:dx:L;
u = sin(pi * x / left_wave_length) + sin(2 * pi * x / right_wave_length);
% Time integration
for step = 1:num_steps
    % Compute second spatial derivative using finite differences
    u_xx = (u(1:end-2) - 2*u(2:end-1) + u(3:end)) / dx^2;
    
    % Update the wave equation using finite differences
    u_new = 2*u(2:end-1) - u(2:end-1) + c^2 * dt^2 * u_xx;
    
    % Update boundary conditions
    u_new1 = [0, u_new, 0];
    
    % Update the wave function
    u = u_new1;
end
% Plot at t = 0
figure;
plot(x, u);
title('Wave Equation at t = 0');
xlabel('Position [L]');
ylabel('Amplitude');
xlim([0, L]);

% Plot at t = 10 [t]
figure;
plot(x, u);
title('Wave Equation at t = 10 [t]');
xlabel('Position [L]');
ylabel('Amplitude');
xlim([0, L]);

[Torsten]

@Bijaya

Choose another code from the internet - this one is completely wrong.

Answer 1

[Drishti]

Hi Bijaya,

While debugging the provided code on my end, I also encountered a similar issue of ‘empty figure’.

The issue can be resolved by utilizing a variable ‘u_prev’ to store the value of wave function from the previous step.

You can refer to the implementation provided below:

% Initialize previous wave function for time-stepping
u_prev = u;
% Time integration
for step = 1:num_steps
 % Compute second spatial derivative using finite differences
    u_xx = (u(1:end-2) - 2*u(2:end-1) + u(3:end)) / dx^2;
    % Update the wave equation using finite differences
    u_new = 2*u(2:end-1) - u_prev(2:end-1) + c^2 * dt^2 * u_xx;
    % Update boundary conditions
    u_new1 = [0, u_new, 0];
    % Update the wave functions
    u_prev = u;
    u = u_new1;
end

The ‘u_prev’ variable will be utilized to calculate the updated value of wave in later steps as demonstrated in the code snippet.

I hope this helps in resolving the issue.