# Heun procedure

The **Heun method** , named after Karl Heun , is a simple method for the numerical solution of initial value problems . It is a one-step process and belongs to the class of the Runge-Kutta processes .

In contrast to the explicit Euler method , the approximation is made using a trapezoid and not a rectangle.

## Procedure

To the numerical solution of the initial value problem:

for an ordinary differential equation using Heun's method, choose a discretization step size , consider the discrete times

and calculate first analogously to the explicit Euler method

and then

what can be formed

The are the approximate values of the actual solution function at times .

is called the step size. If the step size is reduced, the procedural error becomes smaller (i.e., they are closer to the actual function value ). The global error of Heun's method is almost zero; one also speaks of the convergence order 2.

## Similar one-step procedures

- Explicit Euler method (Euler's polygon method )
- Implicit Euler method
- Runge-Kutta method
- Classic Runge-Kutta method