A Convergence Analysis of the Peaceman-Rachford Scheme for Semilinear Evolution Equations

Eskil Hansen, Erik Henningsson

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Sammanfattning

The Peaceman--Rachford scheme is a commonly used splitting method for discretizing semilinear evolution equations, where the vector fields are given by the sum of one linear and one nonlinear dissipative operator. Typical examples of such equations are reaction-diffusion systems and the damped wave equation. In this paper we conduct a convergence analysis for the Peaceman--Rachford scheme in the setting of dissipative evolution equations on Hilbert spaces. We do not assume Lipschitz continuity of the nonlinearity, as previously done in the literature. First or second order convergence is derived, depending on the regularity of the solution, and a shortened proof for $o(1)$-convergence is given when only a mild solution exits. The analysis is also extended to the Lie scheme in a Banach space framework. The convergence results are illustrated by numerical experiments for Caginalp's solidification model and the Gray--Scott pattern formation problem.
Originalspråkengelska
Sidor (från-till)1900-1910
Antal sidor11
TidskriftSIAM Journal on Numerical Analysis
Volym51
Nummer4
DOI
StatusPublished - 2013

Bibliografisk information

The information about affiliations in this record was updated in December 2015.
The record was previously connected to the following departments: Numerical Analysis (011015004)

Ämnesklassifikation (UKÄ)

  • Matematik

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  • Erik Henningsson

    Eskil Hansen (Första/primär/huvudhandledare)

    20112016

    Aktivitet: Examination och handledarskapHandledning av forskarstuderande

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