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

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- by Eskil Hansen and Tony Stillfjord PDF
- Math. Comp.
**82**(2013), 1975-1985 Request permission

## Abstract:

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.## References

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## Additional Information

**Eskil Hansen**- Affiliation: Centre for Mathematical Sciences, Lund University, P.O. Box 118, SE-22100 Lund, Sweden
- Email: eskil@maths.lth.se
**Tony Stillfjord**- Affiliation: Centre for Mathematical Sciences, Lund University, P.O. Box 118, SE-22100 Lund, Sweden
- Email: tony@maths.lth.se
- Received by editor(s): June 17, 2011
- Received by editor(s) in revised form: January 9, 2012
- Published electronically: April 30, 2013
- Additional Notes: The work of the first author was supported by the Swedish Research Council under grant 621-2007-6227.
- © Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp.
**82**(2013), 1975-1985 - MSC (2010): Primary 65J08, 65M15, 47H06
- DOI: https://doi.org/10.1090/S0025-5718-2013-02702-0
- MathSciNet review: 3073188