Differential Equations: Euler's Method (Matlab tutorial)

In this video I'll explain and demonstrate how you can apply Euler's method to solve a differential equation (or a system of differential equations in matlab). Code used: %% Euler's method demonstration % differential equation parameters f = @(t,y) y; % solving dy/dt = y y_init = 1; % with the initial condition y(0) = 1 Tspan = [0 5]; % for t = 0 to 5 for Tstep = [1, 0.1, 0.01, 0.001] % apply euler method [t, y] = euler(f, Tspan, y_init, Tstep); % plotting plot(t, y, linspace(Tspan(1), Tspan(end)), exp(linspace(Tspan(1), Tspan(end)))); legend('Euler method', 'Analytic solution'); grid minor; xlabel('t'), ylabel('y') pause; end Code for the Euler's method function: function [t, y] = euler(fun, Tspan, y_init, Tstep) % initialize t vector t = Tspan(1):Tstep:Tspan(end); % pre allocate y vector y = NaN(length(y_init),length(t)); y(:, 1) = y_init; % initial value for y is given % euler method iterations for k = 2:length(t) y(k) = y(k-1) + Tstep*fun(t(k-1) ,y(k-1)); end