function to code euler's method in matlab

main.m
function [t, y] = euler(f, y0, t0, tf, h)
% Implements Euler's method to solve the IVP:
%   y' = f(t, y), y(t0) = y0
% from t = t0 to t = tf with step size h.
% INPUTS:
%   f  - function handle for the RHS of the ODE y' = f(t, y)
%   y0 - initial condition
%   t0 - initial time
%   tf - final time
%   h  - step size
% OUTPUTS:
%   t - vector containing time steps
%   y - vector containing solution values at each time step

t = t0:h:tf;       % vector of time steps
y = zeros(size(t)); % vector of solution values
y(1) = y0;          % initial condition

for i = 1:length(t)-1
    y(i+1) = y(i) + h*f(t(i), y(i)); % Euler's method
end

end
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main.m
f = @(t, y) -y; % RHS of y' = -y
y0 = 1;         % initial condition
t0 = 0;         % initial time
tf = 5;         % final time
h = 0.1;        % step size

[t, y] = euler(f, y0, t0, tf, h); % solve the IVP

plot(t, y) % plot the solution
xlabel('t')
ylabel('y')
title("Euler's method with h = " + h)
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