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High-order splitting schemes for semilinear evolution equations

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Author

Summary, in English

We first derive necessary and sufficient stiff order conditions, up to order four, for exponential splitting schemes applied to semilinear evolution equations. The main idea is to identify the local splitting error as a sum of quadrature errors. The order conditions of the quadrature rules then yield the stiff order conditions in an explicit fashion, similarly to that of Runge–Kutta schemes. Furthermore, the derived stiff conditions coincide with the classical non-stiff conditions. Secondly, we propose an abstract convergence analysis, where the linear part of the vector field is assumed to generate a group or a semigroup and the nonlinear part is assumed to be smooth and to satisfy a set of compatibility requirements. Concrete applications include nonlinear wave equations and diffusion-reaction processes. The convergence analysis also extends to the case where the nonlinear flows in the exponential splitting scheme are approximated by a sufficiently accurate one-step method.

Department/s

Publishing year

2016

Language

English

Pages

1303-1316

Publication/Series

BIT Numerical Mathematics

Volume

56

Issue

4

Document type

Journal article

Publisher

Springer

Topic

  • Other Mathematics

Keywords

  • Splitting schemes
  • Exponential splitting
  • Semilinear evolution equations
  • High-order methods
  • Stiff orders
  • Convergence

Status

Published

Research group

  • Numerical Analysis
  • Partial differential equations

ISBN/ISSN/Other

  • ISSN: 0006-3835