Question

Write a function-function in MATLAB that use's Euler's Method to determine a numerical solution for a 1st-order ordinary differential equation with one dependent variable using the following line

function [t, y) = EulerIdydt, dt, to, tf, yo]

where

dt = time step

t0 = initial time

tf = final time

y0 = dependent variable for initial value

Answer 1

We have developed a MATLAB code for Euler's Method to determine a numerical solution for a 1st-order ODE.

-------------------------------MATLAB code-------------------------------

function [t,y]=Euler(dydt, dt, t0, tf, y0)

t=t0:dt:tf;
y=0*t;
y(1)=y0;
  
for i=1:numel(t)-1
y(i+1)=y(i)+dt*dydt(t(i),y(i));
end
  
plot(t,y,'LineWidth',1.5);
xlabel('Time (t)')
ylabel('y(t)')
title('t vs y(t)');
end

-------------------------------MATLAB script-------------------------------

dt=0.01;
t0=0;
tf=1;
y0=0;
dydt=@(t,y) 1./(2+2*t.*t);

[t,y]=Euler(dydt, dt, t0, tf, y0);