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A second-order positivity preserving scheme for semilinear parabolic problems

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Author

Summary, in English

In this paper we study the convergence behaviour and geometric properties of Strang splitting applied to semilinear evolution equations. We work in an abstract Banach space setting that allows us to analyse a certain class of parabolic equations and their spatial discretizations. For this class of problems, Strang splitting is shown to be stable and second-order convergent. Moreover, it is shown that exponential operator splitting methods and in particular the method of Strang will preserve positivity in certain situations. A numerical illustration of the convergence behaviour is included.

Department/s

Publishing year

2012

Language

English

Pages

1428-1435

Publication/Series

Applied Numerical Mathematics

Volume

62

Issue

10

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematics

Keywords

  • positivity
  • convergence
  • stability
  • semilinear parabolic problems
  • Strang splitting
  • invariant sets.

Status

Published

Research group

  • Partial differential equations
  • Numerical Analysis

ISBN/ISSN/Other

  • ISSN: 0168-9274