Robust defect control with Runge-Kutta schemes

D.J. Higham

Research output: Contribution to journalArticle

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.
Original languageEnglish
Pages (from-to)1175-1183
Number of pages8
JournalSIAM Journal on Numerical Analysis
Volume26
Issue number5
Publication statusPublished - 1989

Keywords

  • Runge-Kutta formula
  • defect
  • interpolation
  • numerical mathematics

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