# Numerical Solution of Diﬀerential-Algebraic Equations with Application in the Simulation of Cooling Systems

## Marion Lackner

**Jan. 16, 2007, 2:30 p.m. T 1010**

This work is based on a problem that arised in the simulation of cooling systems with the software package Kuli. The underlying model of the transient simulation is described by a system of semi-explicit diﬀerential-algebraic equations of index 1. The aim of the work is the eﬃcient numerical solution of this system. This system of semi-explicit diﬀerential-algebraic equations of index 1 can be reduced to a system of ordinary diﬀerential equations, hence for solving them, it is possible to use conventional numerical methods. Two classes of numerical methods are considered, explicit Runge-Kutta methods and linear multistep methods, especially Adams methods.

In addition to the description and analysis of the numerical methods and their application to semi-explicit diﬀerential-algebraic equations of index 1, also the implementation of the methods is considered, in particular step-size control and dense output.

The numerical experiments were done by implementing already exisiting codes of the methods into Kuli. For a representative model the comparison of the original algorithm and the new one shows a performance increase of at least a factor of ten.