Stepsize selection for tolerance proportionality in explicit Runge-Kutta codes

M.C. Calvo, D.J. Higham, J.M. Montijano, L. Rández

Research output: Contribution to journalArticle

Abstract

The potential for adaptive explicit Runge-Kutta (ERK) codes to produce global errors that decrease linearly as a function of the error tolerance is studied. It is shown that this desirable property may not hold, in general, if the leading term of the locally computed error estimate passes through zero. However, it is also shown that certain methods are insensitive to a vanishing leading term. Moreover, a new stepchanging policy is introduced that, at negligible extra cost, ensures a robust global error behaviour. The results are supported by theoretical and numerical analysis on widely used formulas and test problems. Overall, the modified stepchanging strategy allows a strong guarantee to be attached to the complete numerical process.
Original languageEnglish
Pages (from-to)361-382
Number of pages21
JournalAdvances in Computational Mathematics
Volume7
Issue number3
DOIs
Publication statusPublished - Sep 1997

    Fingerprint

Keywords

  • initial value problems
  • Runge-Kutta methods
  • stepsize control
  • mathematics
  • computer science

Cite this