why am i getting grey figure box can someone fix please

% Constants
g = 9.81;  % Acceleration due to gravity
L = 1.0;   % Length of the pendulum
t = linspace(0, 20, 1000);  % Time vector

% Loop through each initial condition
initial_conditions_list = [0.5; 1.0; 1.5; pi];

for i = 1:length(initial_conditions_list)
    figure;  % Create a new figure for each initial condition
    
    theta0 = initial_conditions_list(i);
    
    % Analytical solution (from A4)
    theta_A4 = theta0 * cos(sqrt(g/L) * t);
    
    % Numerical solution (from A6)
    initial_conditions = [theta0; 0];
    [t_numerical, Y] = ode45(@(t,Y) pendulumODE(t,Y,g,L), [0 20], initial_conditions);
    theta_A6 = Y(:, 1);
    
    % Plotting analytical solution
    plot(t, theta_A4, 'r-', 'LineWidth', 2);
    hold on;
    
    % Plotting numerical solution
    plot(t_numerical, theta_A6, 'b--', 'LineWidth', 2);
    hold off;
    
    xlabel('Time (s)');
    ylabel('Theta (radians)');
    title(['Initial Theta = ', num2str(theta0), ' radians']);
    legend('Analytical Solution', 'Numerical Solution');
    grid on;
end

Unrecognized function or variable 'pendulumODE'.

Error in solution>@(t,Y)pendulumODE(t,Y,g,L) (line 19)
[t_numerical, Y] = ode45(@(t,Y) pendulumODE(t,Y,g,L), [0 20], initial_conditions);

Error in odearguments (line 92)
f0 = ode(t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 104)
odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

[Voss]

Unable to run the code: The function pendulumODE is undefined (see above).

[Sulaymon Eshkabilov]

As @Voss pinpointed the function file or function handle (anonymous function) called pendulumODE(t,Y,g,L) is missing.

It can be defined as an anonymous function or function file per se.

Answer 1

[Alan Stevens]

Making some assumptions about your function pendulumODE, I think the following is more like what you expect to see:

% Constants
g = 9.81;  % Acceleration due to gravity
L = 1.0;   % Length of the pendulum
t = linspace(0, 20, 100);  % Time vector

% Loop through each initial condition
initial_conditions_list = [0.5; 1.0; 1.5; pi];

for i = 1:length(initial_conditions_list)
    figure;  % Create a new figure for each initial condition
    
    theta0 = initial_conditions_list(i);
    
    % Analytical solution (from A4)
    w = sqrt(g/L);
    theta_A4 = theta0 * cos(w * t);
    
    % Numerical solution (from A6)
    initial_conditions = [theta0; 0];
    [t_numerical, Y] = ode45(@(t,Y) pendulumODE(t,Y,g,L), [0 20], initial_conditions);
    theta_A6 = Y(:,1);
    
    % Plotting analytical solution
    plot(t, theta_A4, 'r-', 'LineWidth', 2);
    hold on;
    
    % Plotting numerical solution
    plot(t_numerical, theta_A6, 'b--', 'LineWidth', 2);
    hold off;
    
    xlabel('Time (s)');
    ylabel('Theta (radians)');
    title(['Initial Theta = ', num2str(theta0), ' radians']);
    legend('Analytical Solution', 'Numerical Solution');
    grid on;
end

function dthetavdt = pendulumODE(~,Y,g,L)
        theta = Y(1); v = Y(2);
        w = sqrt(g/L);
        dthetavdt = [v; -w^2*theta];
        
end