# Forward Euler Method

We have the Initial Value Problem $y_{′}(t)=f(t,y(t))withy(t_{0})=y_{0}$

and we assume that we have a given set of $t$ points $t_{0}<t_{1}<⋯<t_{N}$ with our problem being to find the $y_{i}$.

Forward Euler Scheme

The Forward Euler Scheme is

$y_{n+1}=y_{n}+hf(t_{n},y_{n})$ where $h=t_{n+1}−t_{n}$

The Forward Euler method is the simplest technique for obtaining a numerical approximation to a first order initial value problem.