euler method with more than one step value in matlab

The Euler's method is a simple numerical method to approximate the solutions of ordinary differential equations (ODEs). It can be extended to use more than one step value by updating the solution iteratively.

Here is an example of how to implement the Euler's method with multiple step values in MATLAB:

main.m
function [t, y] = eulerMethod(f, a, b, y0, h)
    % f is the differential equation function
    % a and b are the start and end values of the independent variable
    % y0 is the initial value of the dependent variable
    % h is the step size

    % Calculate the number of steps
    n = floor((b - a) / h);

    % Initialize arrays
    t = zeros(n+1, 1);
    y = zeros(n+1, 1);

    % Set initial values
    t(1) = a;
    y(1) = y0;

    % Euler's method iteration
    for i = 1:n
        t(i+1) = t(i) + h;
        y(i+1) = y(i) + h * f(t(i), y(i));
    end
end
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To use the above function, you need to define your differential equation f, the start and end values a and b, the initial value y0, and the step size h. For example, let's consider the simple ODE dy/dt = t.

main.m
f = @(t, y) t;   % Define the differential equation
a = 0;           % Start value of t
b = 1;           % End value of t
y0 = 0;          % Initial value of y
h = 0.1;         % Step size

[t, y] = eulerMethod(f, a, b, y0, h);   % Call the Euler's method function

% Plot the results
plot(t, y)
xlabel('t')
ylabel('y')
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This code will approximate the solution to the dy/dt = t differential equation using Euler's method with a step size of 0.1. You can adjust the step size h to get a more accurate approximation.

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