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On the convergence of Lawson methods for semilinear stiff problems

Hochbruck, Marlis; Leibold, Jan; Ostermann, Alexander

Abstract:
Since their introduction in 1967, Lawson methods have achieved constant interest in the time discretization of evolution equations. The methods were originally devised for the numerical solution of stiff differential equations. Meanwhile, they constitute a well-established class of exponential integrators, which has turned out to be competitive for solving space discretizations of certain types of partial differential equations. The popularity of Lawson 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. ... mehr

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Verlagsausgabe §
DOI: 10.5445/IR/1000122245
Veröffentlicht am 29.07.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 07.2020
Sprache Englisch
Identifikator ISSN: 0029-599X, 0945-3245
KITopen-ID: 1000122245
Erschienen in Numerische Mathematik
Band 145
Heft 3
Seiten 553–580
Vorab online veröffentlicht am 25.05.2020
Nachgewiesen in Web of Science
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