euler method with multiple step values in matlab

To implement the Euler method with multiple step values in MATLAB, you can use a loop to iterate through each step, updating the solution at each iteration. Here is an example code snippet that demonstrates how to do this:

main.m
% Define the initial conditions and parameters
t0 = 0;         % initial time
tf = 1;         % final time
h_values = [0.1, 0.05, 0.01];  % multiple step values
y0 = 1;         % initial condition

% Loop over each step size
for h = h_values
    num_steps = (tf - t0) / h;  % calculate the number of steps
    
    % Initialize the time and solution arrays
    t = t0:h:tf;
    y = zeros(size(t));
    y(1) = y0;
    
    % Perform the Euler method iterations
    for i = 1:num_steps
        y(i+1) = y(i) + h * f(t(i), y(i));  % update the solution using Euler's method
    end
    
    % Plot the solution for the current step size
    figure;
    plot(t, y);
    xlabel('t');
    ylabel('y');
    title(['Euler Method with h = ', num2str(h)]);
    
end

% Define the function f(t, y) that represents the derivative of y
function dydt = f(t, y)
    dydt = -2 * t * y;
end
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In this code, we define the initial conditions and parameters, including the initial and final time and the desired step values. We then loop over each step value and perform the Euler method iterations within the inner loop. Finally, we plot the solution for each step size.

Note: In the code above, the function f(t, y) represents the derivative of y with respect to t. You can modify this function to match your specific differential equation.

Make sure to replace the f(t, y) function with the appropriate derivative function for your specific problem. Additionally, you can customize the code to suit your particular requirements, such as adding additional plots or modifying the plot titles and labels.