forward euler in matlab

The forward Euler method is a numerical method used to solve first-order ordinary differential equations (ODEs) with a given initial value. It is a simple and straight-forward method that computes the next value of the dependent variable using the previous value and the derivative of the function at that point. Here is the code for implementing the forward Euler method in Matlab:

% Define the initial value and time step
y(1) = y0;    % initial value
t(1) = t0;    % initial time
h = (tf - t0)/N;   % time step

% Compute the solution using the forward Euler method
for i=1:N
    y(i+1) = y(i) + h*f(y(i), t(i));   % Update y
    t(i+1) = t(i) + h;                 % Update t
end

% Plot the solution
plot(t, y);
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In this code, y0 is the initial value of the dependent variable, t0 is the initial time, and tf is the final time. N is the number of time steps, and h is the time step size. The f function is the derivative of the function that we want to solve. Note that the y(i+1) and t(i+1) generate the sequence of time and solution pairs.

This code can be modified for specific ODEs by changing the f function.