Forward Euler

Topics: Numerical Methods

The forward Euler method is a first-order numerical procedure used to solve ordinary differential equations (ODEs) with a given initial value. It estimates the future value of a system by taking a small step along the current slope.

For the ODE problem $\frac{dy}{dt}=f(t,y)$ with initial condition $y(t_0) = y_0$, Forward Euler advances the numerical simulation from $t_n$ to $t_{n+1}=t_n+h$ as
$y_{n+1}=y_n + h \cdot f(t_n, y_n)$
The above formula can be used to compute a running integral from data.

Forward Euler is an explicit method because all the information needed to compute the approximation at $t_{n+1}$ is already known at $t_n$.

Geometric Interpretation: the slope is taken at the beginning of the interval and is held constant during the step.

References

1. https://web.mit.edu/10.001/Web/Course_Notes/Differential_Equations_Notes/node3.html