BIT Numerical Mathematics

, Volume 38, Issue 3, pp 462–485

On variable stepsize Runge-Kutta approximations of a Cauchy problem for the evolution equation

  • Nikolai Yu. Bakaev
Article

DOI: 10.1007/BF02510254

Cite this article as:
Bakaev, N.Y. Bit Numer Math (1998) 38: 462. doi:10.1007/BF02510254

Abstract

We consider a Cauchy problem for the sectorial evolution equation with generally variable operator in a Banach space. Variable stepsize discretizations of this problem by means of a strongly A(φ)-stable Runge-Kutta method are studied. The stability and error estimates of the discrete solutions are derived for wider families of nonuniform grids than quasiuniform ones (in particular, if the operator in question is constant or Lipschitz-continuous, for arbitrary grids).

AMS subject classification

65J10 65N12 

Key words

Evolution equation sectorial operator Runge-Kutta method Cauchy problem variable stepsize approximations stability estimates error estimates 

Copyright information

© Swets & Zeitlinger 1998

Authors and Affiliations

  • Nikolai Yu. Bakaev
    • 1
  1. 1.Department of MathematicsAir-Force Engineering AcademyMoscowRussia

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