Robust defect control with Runge-Kutta schemes

Higham, D.J. (1989) Robust defect control with Runge-Kutta schemes. SIAM Journal on Numerical Analysis, 26 (5). pp. 1175-1183. ISSN 0036-1429 (http://locus.siam.org/SINUM/volume-26/art_0726065....)

Abstract

Enright [Numerical Analysis Report 122, University of Manchester, Manchester, U.K., 1986] implements a Runge-Kutta method for solving the initial value problem using an alternative to the standard local error control scheme. The aim is to control the defect associated with a local interpolant by sampling its value at one or more fixed points within each step. However, in general, the quality of a sample point is problem-dependent and also varies from step to step. Two classes of interpolant are presented for which the asymptotic behaviour of the defect is known a priori, allowing optimal sample points to be chosen.

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• Item metadata

  Item type:	Article
  ID code:	211
  Dates:	Date Event 1989 Published
  Subjects:	Science > Mathematics
  Department:	Faculty of Science > Mathematics and Statistics
  Depositing user:	Ms Sarah Scott
  Date deposited:	08 Mar 2006
  Last modified:	08 Apr 2024 15:15
  Related URLs:	http://locus.siam.org/fulltext/SINUM/vol...
  URI:	https://strathprints.strath.ac.uk/id/eprint/211