What can I do?

% Define the parameters of the problem 
L = 80; % length of the string (cm) 
mu = 0.0125; % linear mass density of the string (g/cm) 
T = 40000; % tension in the string (g) 
c = sqrt(T/mu); % speed of the wave (cm/s) 
x0 = 20; % initial displacement point (cm) 
y0 = 0.6; % initial displacement (cm) 
Ax = 10; % spatial step size (cm) 
At = 0.000179; % time step size (s) 
N = L/Ax + 1; % number of spatial grid points 
M = 2*N; % number of time steps (2 cycles)
% Initialize the arrays 
y = zeros(N, M); % y(x, t) array 
x = linspace(0, L, N); % x array
% Set the initial conditions 
y(:, 1) = x.*(y0/x0); % linear displacement profile 
y(x0/Ax + 1, 1) = y0; % initial displacement point
% Use the finite difference method to approximate the wave equation 
for n = 2:M 
    for i = 2:N-1  
        y(i,n) = 2*y(i, n-1) -y(i, n-2)+ (c*At/Ax)^2*(y(i+1, n-1)-2*y(i,n-1)+ y(i-1,n-1)); 
    end
    % Apply boundary conditions 
    y(1, n) = y(2, n); 
    y(N, n) = y(N-1, n); 
end

Index in position 2 is invalid. Array indices must be positive integers or logical values.

% Plot the results 
t = linspace(0, M*At, M); 
figure; 
plot(x, y(:, 1), 'b-', x, y(:, M), 'r-'); 
xlabel('Position (cm)'); 
ylabel('Displacement (cm)'); 
legend('t = 0', 't = 2 cycles'); 
title('Vibration of Banjo String');
% Calculate the frequency of vibration 
cycle_time = 2*M*At; % time for 2 cycles 
frequency = 1/cycle_time; % frequency in cycles/sec 
disp(['Frequency of vibration: ' num2str(frequency) ' cycles/sec']);

Answer 1

[Torsten]

y(i,n) = 2*y(i, n-1) -y(i, n-2)+ (c*At/Ax)^2*(y(i+1, n-1)-2*y(i,n-1)+ y(i-1,n-1));

For n = 2 and i = 2, you try to access y(2,0) which throws an error.

[Nuha Krir]

it doesn't work

[Walter Roberson]

@Nuha Krir

You have

for n = 2:M 
    for i = 2:N-1  
        y(i,n) = 2*y(i, n-1) -y(i, n-2)+ (c*At/Ax)^2*(y(i+1, n-1)-2*y(i,n-1)+ y(i-1,n-1)); 
    end

When n == 2 then n-2 is 0 so you would be trying to access y(i, 0) which is not valid in MATLAB.

There are two possibilities:

1. That your y update code is incorrect; Or
2. That your n needs to start at 3.

[Nuha Krir]

Thanks alot