How to avoid order reduction when Lawson methods integrate nonlinear initial boundary value problems

It is well known that Lawson methods suffer from a severe order reduction when integrating initial boundary value problems where the solutions are not periodic in space or do not satisfy enough conditions of annihilation on the boundary. However, in a previous paper, a modification of Lawson quadrat...

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Bibliographic Details
Published inBIT Vol. 62; no. 2; pp. 431 - 463
Main Authors Cano, B., Reguera, N.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.06.2022
Springer Nature B.V
Subjects
Boundary conditions
Boundary value problems
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
Numeric Computing
Quadratures
Runge-Kutta method
Order reduction
Lawson methods
Initial boundary value problems
65M12
65M20
Reaction-diffusion
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Summary:It is well known that Lawson methods suffer from a severe order reduction when integrating initial boundary value problems where the solutions are not periodic in space or do not satisfy enough conditions of annihilation on the boundary. However, in a previous paper, a modification of Lawson quadrature rules has been suggested so that no order reduction turns up when integrating linear problems subject to time-dependent boundary conditions. In this paper, we describe and thoroughly analyse a technique to avoid also order reduction when integrating nonlinear problems. This is very useful because, given any Runge–Kutta method of any classical order, a Lawson method can be constructed associated to it for which the order is conserved.
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ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-021-00879-8