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UBC Theses and Dissertations

Implementation methods for singularly perturbed two-point boundary value problems Jacobs, Simon


In this thesis we consider the numerical solution of singularly perturbed two-point boundary value problems in ordinary differential equations. We examine implementation methods for general purpose solvers of first order linear systems. The basic difference scheme is collocation at Gauss points, with a new symmetric Runge-Kutta implementation. Adaptive mesh selection is based on localized error estimates at the collocation points. These methods are implemented as modifications to the successful collocation code, COLSYS (Ascher, Christiansen & Russell), which was designed for mildly stiff problems only. Efficient high order approximations to extremely stiff problems are obtained, and comparisons to COLSYS show that the modifications work much better as the singular perturbation parameter gets small (i.e. the problem gets stiff), for both boundary layer and turning point problems.

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