Webbläsaren som du använder stöds inte av denna webbplats. Alla versioner av Internet Explorer stöds inte längre, av oss eller Microsoft (läs mer här: * https://www.microsoft.com/en-us/microsoft-365/windows/end-of-ie-support).

Var god och använd en modern webbläsare för att ta del av denna webbplats, som t.ex. nyaste versioner av Edge, Chrome, Firefox eller Safari osv.

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

In English

Författare

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.

Avdelning/ar

Publiceringsår

2013

Språk

Engelska

Sidor

1975-1985

Publikation/Tidskrift/Serie

Mathematics of Computation

Volym

82

Issue

284

Dokumenttyp

Artikel i tidskrift

Förlag

American Mathematical Society (AMS)

Ämne

  • Mathematics

Nyckelord

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

Status

Published

Forskningsgrupp

  • Numerical Analysis
  • Partial differential equations

ISBN/ISSN/Övrigt

  • ISSN: 1088-6842