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UBC Theses and Dissertations

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UBC Theses and Dissertations

An algorithm for solving index 1 differential algebraic equations in boundary value problems Chan, Pat S. Y.

Abstract

In this thesis we consider the numerical solution of boundary value problems for differential algebraic equations (DAEs) of index 1. It was shown in Ascher [1], [2], that if symmetric schemes are used for linear index 1 DAEs, the stability is controlled by the stability of an auxiliary (ghost) differential problem which is not necessarily stable even if the given problem is. We examine an algorithm which preserves the stability of the ghost problem by arranging the auxiliary boundary conditions properly. The algorithm has been implemented in a code (DAESOLVE) and tested on numerous examples. This code has been compared with a code which chooses the boundary conditions arbitrarily, showing favourable results.

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