## 06-45

#### Automatic step size selection for the fractional-step-theta-scheme

by Rang, J.

Preprint series: 06-45, Preprints

MSC:
Abstract: In this note the fractional-step-$\theta$-scheme is written as a diagonally implicit Runge-Kutta method (DIRK method). In this context a strongly A-stable embedded formula of order one is created such that an ODE or a DAE can be solved with automatic step length control. Moreover the implementation of Runge-Kutta methods applied on DAEs of index 2 is explained. Finally, we apply the new method with automatic step size control on the incompressible Navier-Stokes equations. The numerical results show the advantage of the method.
Keywords: imcompressible Navier-Stokes equations, implicit $\theta$-schemes, Runge-Kutta-methods, order reduction