Heun's method

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

In contrast to the Explicit Euler method, the approximation over a trapezoid and not a rectangle is done.

Method

For the numerical solution of the initial value problem:

For an ordinary differential equation by the method of Heun you choose a discretization step size, consider the discrete time points

And calculate initially analogous to the forward Euler method

And then

What to can be worked

Which are the approximate values ​​of the actual solution function at the time points.

Is called the step size. If we reduce the step size, the method error is smaller (read: closer to the actual function value x (ti) ). The global error of the method of Heun goes to zero; we also speak of convergence order 2

Similar one-step method

  • Explicit Euler method ( Eulerian Polygonzugverfahren )
  • Implicit Euler method
  • Runge- Kutta method
  • Classic Runge- Kutta methods
Backward Euler method
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