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On the convergence of Laws on methods for semilinear stiff problems

Hochbruck, Marlis; Ostermann, Alexander

Abstract:
Since their introduction in 1967, Lawson methods have attracted continuous interest for the time discretization of evolution equations. The popularity of these methods is in some contrast to the fact that they may have a bad convergence behaviour, since they do not satisfy any of the stiff order conditions. The aim of this paper is to explain this discrepancy. It is shown that non-stiff order conditions together with appropriate regularity assumptions imply high-order convergence of Lawson methods. Note, however, that the term regularity here includes the behaviour of the solution at the boundary. For instance, Lawson methods will behave well in the case of periodic boundary conditions, but they will show a dramatic order reduction for, e.g., Dirichlet boundary conditions. The precise regularity assumptions required for high-order convergence are worked out in this paper and related to the corresponding assumptions for splitting schemes. In contrast to previous work the analysis is based on expansions of the exact and the numerical solution along the flow of the homogeneous problem. Numerical examples for the Schrödinger equation ar ... mehr


Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2017
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000068916
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-689164
KITopen ID: 1000068916
Verlag KIT, Karlsruhe
Umfang 15 S.
Serie CRC 1173 ; 2017/9
Schlagworte exponential integrators, Lawson methods, linear and nonlinear Schrödinger equations, evolution equations, order conditions
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