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High order splitting methods for analytic semigroups exist

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Author

Summary, in English

In this paper, we are concerned with the construction and analysis of high order exponential splitting methods for the time integration of abstract evolution equations which are evolved by analytic semigroups. We derive a new class of splitting methods of orders three to fourteen based on complex coefficients. An optimal convergence analysis is presented for the methods when applied to equations on Banach spaces with unbounded vector fields. These results resolve the open question whether there exist splitting schemes with convergence rates greater then two in the context of semigroups. As a concrete application we consider parabolic equations and their dimension splittings. The sharpness of our theoretical error bounds is further illustrated by numerical experiments.

Department/s

Publishing year

2009

Language

English

Pages

527-542

Publication/Series

BIT Numerical Mathematics

Volume

49

Issue

3

Document type

Journal article

Publisher

Springer

Topic

  • Mathematics

Keywords

  • High order convergence
  • Exponential splitting methods
  • Analytic semigroups
  • Parabolic equations

Status

Published

Research group

  • Partial differential equations
  • Numerical Analysis

ISBN/ISSN/Other

  • ISSN: 0006-3835