On the development of effective algorithms for the numerical solution of singularly perturbed two-point boundary value problems
by Steven Capper, Jeff Cash, Francesca Mazzia
International Journal of Computing Science and Mathematics (IJCSM), Vol. 1, No. 1, 2007

Abstract: Singular perturbation boundary value problems have proved to be hard to solve numerically because their solutions have regions of rapid variation. Extensive numerical experience has shown that it is important to consider the conditioning of such problems since algorithms are developed on the assumption that a small local error in the computed solution will produce a correspondingly small global error. This may be valid only if the problem is well conditioned. In this paper we describe how conditioning information can be added to state of the art codes, and give numerical results demonstrating the effectiveness of this approach.

Online publication date: Fri, 25-May-2007

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