Convergence of the implicit-explicit Euler scheme applied to perturbed dissipative evolution equations
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
- Matematik LTH
- Numerical Analysis
- Partial differential equations
Publiceringsår
2013
Språk
Engelska
Sidor
1975-1985
Publikation/Tidskrift/Serie
Mathematics of Computation
Volym
82
Issue
284
Fulltext
- Available as PDF - 168 kB
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Länkar
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