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Accuracy estimates for computer algebra system initial-value problem (IVP) solvers

Stephan V. Joubert
Organization: Tshwane University of Technology, Arcadia Campus, South Africa
JC Greeff
Journal / Anthology

Year: 2006
Volume: 102
Issue: 1-2
Page range: 46-50

Many computer algebra systems (CASs) include ready-to-use numerical initial-value problem (IVP) solvers. However, even experienced mathematical scientists have fallen into the trap of using the available technology without questioning the accuracy of the solutions generated. In this paper, we outline an error analysis that anyone, with a working knowledge of an IVP solver and of basic calculus, can implement with ease. The method outlined not only attempts to estimate the accuracy of a solution to an IVP (satisfying some mild existence condition) given by the 'NDSolve' algorithm of Mathematica (R), but has an added bonus: it usually also indicates visually on which part of the domain of the solution the algorithm appears to be working properly and where it might be struggling. This method should be adaptable to other CASs. This article has been written with a broad audience in mind. It is not intended exclusively for those numerical analysts with an in-depth knowledge of how to check the accuracy of numerical routines.

*Applied Mathematics > Numerical Methods

computer algebra system, initial-value problem solvers, error analysis, Duffing's equation