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High-order splitting schemes for semilinear evolution equations

In English

Författare

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.

Avdelning/ar

Publiceringsår

2016

Språk

Engelska

Sidor

1303-1316

Publikation/Tidskrift/Serie

BIT Numerical Mathematics

Volym

56

Issue

4

Dokumenttyp

Artikel i tidskrift

Förlag

Springer

Ämne

  • Other Mathematics

Nyckelord

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

Status

Published

Forskningsgrupp

  • Numerical Analysis
  • Partial differential equations

ISBN/ISSN/Övrigt

  • ISSN: 0006-3835