multiple euler plots in matlab

To plot multiple Euler plots in MATLAB, you can use a loop to generate the data for each plot and then plot them using the plot function.

Here is an example code that demonstrates how to plot multiple Euler plots:

main.m
% Define the differential equation and initial condition
dy_dt = @(t, y) -0.1 * y;
y0 = 100;

% Define the time interval
tspan = [0 10];

% Define the step sizes for each plot
step_sizes = [1 0.1 0.01];

figure; % Create a new figure

% Loop through each step size
for i = 1:length(step_sizes)
    h = step_sizes(i);
    
    % Solve the differential equation using Euler's method
    [t, y] = euler(dy_dt, tspan, y0, h);
    
    % Plot the solution
    plot(t, y, 'DisplayName', sprintf('Step Size = %.2f', h));
    hold on;
end

hold off;
title('Multiple Euler Plots');
xlabel('Time');
ylabel('y');
legend('Location','best');

% Euler's Method implementation
function [t, y] = euler(dy_dt, tspan, y0, h)
    t = tspan(1):h:tspan(2);
    y = zeros(1, length(t));
    y(1) = y0;
    
    for i = 2:length(t)
        y(i) = y(i-1) + h * dy_dt(t(i-1), y(i-1));
    end
end
872 chars
41 lines

In this example, the differential equation dy_dt is defined as -0.1 * y, and the initial condition y0 is set to 100. The time interval tspan is set from 0 to 10. The step sizes for each plot are defined in the step_sizes array.

Inside the loop, the euler function is called to solve the differential equation using Euler's method for each step size. The solution is then plotted using the plot function, with a different display name for each plot to distinguish them in the legend.

Finally, the figure title, x-axis label, y-axis label, and legend are added to the plot.

Make sure to replace dy_dt with your own differential equation function and adjust the parameters according to your needs.

Note: This code assumes that the euler function is defined in the MATLAB workspace or in a separate file that is added to the MATLAB path.