euler's method function in matlab

Euler's method is a numerical method for solving differential equations. Here is an example function in MATLAB that implements Euler's method:


main.m
function [t, y] = euler_method(f, y0, t0, tf, h)
% Euler's method for solving y' = f(t, y), y(t0) = y0
% f: function handle for the right-hand side
% y0: initial condition
% t0: starting time
% tf: ending time
% h: step size

t = t0:h:tf; % array of t values
y = zeros(size(t)); % array of y values
y(1) = y0; % set initial condition

for i = 1:length(t)-1
    y(i+1) = y(i) + h*f(t(i), y(i)); % Euler's method update
end
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You can call this function by specifying the right-hand side function f, initial condition y0, starting time t0, ending time tf, and step size h. For example, to solve the differential equation y' = -2ty, y(0) = 1 from t = 0 to t = 1 with step size h = 0.1, you can use the following code:


main.m
f = @(t, y) -2*t*y; % right-hand side function
y0 = 1; % initial condition
t0 = 0; % starting time
tf = 1; % ending time
h = 0.1; % step size

[t, y] = euler_method(f, y0, t0, tf, h); % call euler_method function

plot(t, y); % plot the solution
xlabel('t'); ylabel('y'); title('Euler''s method');
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