Time-Stepping Methods

Improved Forward Euler Method

This combines Forward Euler Method with Trapezoidal Rule.

Use average of slope at start and (approximate) end.

We use these two equations:

1. The Forward Euler Step $y_{n+1}^{\ast }=y_n+hf(t_n,y_n)$
2. The Trapezoidal Rule (turning it explicit using the value from step 1) $y_{n+1}=y_n+\frac{h}{2}(f(t_n,y_n)+f(t_{n+1},y_{n+1}^{\ast }))$

Local truncation error of $O(h^3)$.

Related

• Trapezoidal Method