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Convergence of the implicit-explicit Euler scheme applied to perturbed dissipative evolution equations

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Author

Summary, in English

We present a convergence analysis for the implicit-explicit (IMEX) Euler discretization of nonlinear evolution equations. The governing vector field of such an equation is assumed to be the sum of an unbounded dissipative operator and a Lipschitz continuous perturbation. By employing the theory of dissipative operators on Banach spaces, we prove that the IMEX Euler and the implicit Euler schemes have the same convergence order, i.e., between one half and one depending on the initial values and the vector fields. Concrete applications include the discretization of diffusion-reaction systems, with fully nonlinear and degenerate diffusion terms. The convergence and efficiency of the IMEX Euler scheme are also illustrated by a set of numerical experiments.

Department/s

Publishing year

2013

Language

English

Pages

1975-1985

Publication/Series

Mathematics of Computation

Volume

82

Issue

284

Document type

Journal article

Publisher

American Mathematical Society (AMS)

Topic

  • Mathematics

Keywords

  • Implicit-explicit Euler scheme
  • convergence orders
  • nonlinear evolution equations
  • dissipative operators

Status

Published

Research group

  • Numerical Analysis
  • Partial differential equations

ISBN/ISSN/Other

  • ISSN: 1088-6842