Time-Stepping Method

Forward Euler Method

We have the Initial Value Problem $y^{\prime }(t)=f(t,y(t))\text{with}y(t_0)=y_0$

and we assume that we have a given set of $t$ points $t_0<t_1<\cdots <t_N$ 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.