Title
The Treatment of Derivative Discontinuities in Differential Equations
Authors
Christopher A.H. Paul
Keywords
Differential equations, discontinuities, numerical solution
Report No.
337
Date
6th January 1999
Status
Published in Proceedings of 4th Hellenic European Conference on Computer Mathematics and its Applications 1998
File size
113Kb
Abstract
The assumption of sufficiently smooth derivatives underlies much of the analysis of numerical methods for both ordinary and delay differential equations. However, derivative discontinuities can arise in ordinary differential equations and usually do arise in delay differential equations. In this paper, I review two of the approaches for treating derivative discontinuities, ``tracking'' using the discontinuity tracking equations and ``detection and location'' using defect error control. I conclude that neither approach is ideal when it comes to the treatment of derivative discontinuities in delay differential algebraic equations.
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