Error ---> Brace indexing is not supported for variables of this type.

Please any help would be much appreciated. I cant get rid of this error message

clc
clear

g = 9.81;
L = 0.1;
m = 0.5;
zeta = 2;
x0 = 0.25;
v0 = 0;

tspan = [0 10];

step_sizes = [0.1, 0.05, 0.025];

num_steps = numel(step_sizes);
x_euler = cell(1, num_steps);
x_midpoint = cell(1, num_steps);
times_euler = zeros(1, num_steps);
times_midpoint = zeros(1, num_steps);

ode_func = @(t, y) [y(2); (-zeta * y(2) - (m * g * L * y(1))) / m];

for i = 1:num_steps
    tic;
    [t_euler, x_euler{i}] = euler(ode_func, tspan, [x0; v0], step_sizes(i));
    times_euler(i) = toc;
end

for i = 1:num_steps
    tic;
    [t_midpoint, x_midpoint{i}] = midpoint(ode_func, tspan, [x0; v0], step_sizes(i));
    times_midpoint(i) = toc;
    disp(['Length of t_midpoint{' num2str(i) '}: ' num2str(length(t_midpoint))]);
    
end

Length of t_midpoint{1}: 101
Length of t_midpoint{2}: 201
Length of t_midpoint{3}: 401

figure;
hold on;

for i = 1:num_steps
    if numel(t_euler) == numel(t_midpoint{i})
        plot(t_euler, x_euler{i}(:, 1), 'DisplayName', ['Euler (h=' num2str(step_sizes(i)) ')']);
        plot(t_midpoint{i}, x_midpoint{i}(:, 1), 'DisplayName', ['Midpoint (h=' num2str(step_sizes(i)) ')']);
    else
        disp("Error: Unequal number of time points between Euler and Midpoint methods.");
        break;
    end
    disp(['Size of t_midpoint{' num2str(i) '}: ' num2str(size(t_midpoint{i}))]);
    disp(['Size of x_midpoint{' num2str(i) '}: ' num2str(size(x_midpoint{i}))]);
end

Brace indexing is not supported for variables of this type.

xlabel('Time');
ylabel('Position');
title('Comparison of Euler vs Midpoint Method');
legend('Location', 'best');
hold off;

disp('Computation times for Euler Method:');
disp(times_euler);
disp('Computation times for Midpoint Method:');
disp(times_midpoint);



function [t, y] = euler(ode_func, tspan, y0, h)
    t = tspan(1):h:tspan(2);
    n = numel(t);
    y = zeros(n, numel(y0));
    y(1, :) = y0;
    for i = 2:n
        t_i = t(i);
        y(i, :) = y(i-1, :) + h * ode_func(t_i, y(i-1, :)')';
    end
end

function [t, y] = midpoint(ode_func, tspan, y0, h)
    t = tspan(1):h:tspan(2);
    n = numel(t);
    y = zeros(n, numel(y0));
    y(1, :) = y0;
    for i = 2:n
        t_i = t(i);
        k1 = ode_func(t_i, y(i-1, :)');
        k2 = ode_func(t_i + h/2, (y(i-1, :) + (h/2) * k1)');   
        y(i, :) = y(i-1, :) + h * k2';
    end
end

Answer 1

[Torsten]

clc
clear

g = 9.81;
L = 0.1;
m = 0.5;
zeta = 2;
x0 = 0.25;
v0 = 0;

tspan = [0 10];

step_sizes = [0.1, 0.05, 0.025];

num_steps = numel(step_sizes);
x_euler = cell(1, num_steps);
x_midpoint = cell(1, num_steps);
times_euler = zeros(1, num_steps);
times_midpoint = zeros(1, num_steps);

ode_func = @(t, y) [y(2); (-zeta * y(2) - (m * g * L * y(1))) / m];

for i = 1:num_steps
    tic;
    [t_euler{i}, x_euler{i}] = euler(ode_func, tspan, [x0; v0], step_sizes(i));
    times_euler(i) = toc;
end

for i = 1:num_steps
    tic;
    [t_midpoint{i}, x_midpoint{i}] = midpoint(ode_func, tspan, [x0; v0], step_sizes(i));
    times_midpoint(i) = toc;
    disp(['Length of t_midpoint{' num2str(i) '}: ' num2str(numel(t_midpoint{i}))]);
    
end

Length of t_midpoint{1}: 101
Length of t_midpoint{2}: 201
Length of t_midpoint{3}: 401

figure;
hold on;
for i = 1:num_steps
    if numel(t_euler{i}) == numel(t_midpoint{i})
        plot(t_euler{i}, x_euler{i}(:, 1), 'DisplayName', ['Euler (h=' num2str(step_sizes(i)) ')']);
        plot(t_midpoint{i}, x_midpoint{i}(:, 1), 'DisplayName', ['Midpoint (h=' num2str(step_sizes(i)) ')']);
    else
        disp("Error: Unequal number of time points between Euler and Midpoint methods.");
        break;
    end
    disp(['Size of t_midpoint{' num2str(i) '}: ' num2str(size(t_midpoint{i}))]);
    disp(['Size of x_midpoint{' num2str(i) '}: ' num2str(size(x_midpoint{i}))]);
end

Size of t_midpoint{1}: 1  101

Size of x_midpoint{1}: 101    2

Size of t_midpoint{2}: 1  201

Size of x_midpoint{2}: 201    2

Size of t_midpoint{3}: 1  401

Size of x_midpoint{3}: 401    2

xlabel('Time');
ylabel('Position');
title('Comparison of Euler vs Midpoint Method');
legend('Location', 'best');
hold off;

disp('Computation times for Euler Method:');

Computation times for Euler Method:

disp(times_euler);

    0.0033    0.0011    0.0005

disp('Computation times for Midpoint Method:');

Computation times for Midpoint Method:

disp(times_midpoint);

    0.0039    0.0019    0.0009

function [t, y] = euler(ode_func, tspan, y0, h)
    t = tspan(1):h:tspan(2);
    n = numel(t);
    y = zeros(n, numel(y0));
    y(1, :) = y0;
    for i = 2:n
        t_i = t(i);
        y(i, :) = y(i-1, :) + h * ode_func(t_i, y(i-1, :)')';
    end
end

function [t, y] = midpoint(ode_func, tspan, y0, h)
    t = tspan(1):h:tspan(2);
    n = numel(t);
    y = zeros(n, numel(y0));
    y(1, :) = y0;
    for i = 2:n
        t_i = t(i);
        k1 = ode_func(t_i, y(i-1, :)');
        k2 = ode_func(t_i + h/2, (y(i-1, :) + (h/2) * k1)');   
        y(i, :) = y(i-1, :) + h * k2';
    end
end