A New Class of Uniformly Accurate Numerical Schemes for Highly Oscillatory Evolution Equations

We introduce a new methodology to design uniformly accurate methods for oscillatory evolution equations. The targeted models are envisaged in a wide spectrum of regimes, from non-stiff to highly oscillatory. Thanks to an averaging transformation, the stiffness of the problem is softened, allowing fo...

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Bibliographic Details
Published inFoundations of computational mathematics Vol. 20; no. 1; pp. 1 - 33
Main Authors Chartier, Philippe, Lemou, Mohammed, Méhats, Florian, Vilmart, Gilles
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2020
Springer
Springer Nature B.V
Springer Verlag
Subjects
Applications of Mathematics
Computer Science
Differential equations, Nonlinear
Economics
Evolution
Linear and Multilinear Algebras
Math Applications in Computer Science
Mathematical research
Mathematics
Mathematics and Statistics
Matrix Theory
Numerical Analysis
Stiffness
France
Standard averaging
Uniform accuracy
Highly oscillatory problems
Stroboscopic averaging
65L20
35K15
Pullback method
74Q10
Micro–macro method
uniform accuracy AMS subject classification : 65L20
pullback method
standard averaging
uniform accuracy
stroboscopic averaging
micro-macro method
highly-oscillatory problems
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Summary:We introduce a new methodology to design uniformly accurate methods for oscillatory evolution equations. The targeted models are envisaged in a wide spectrum of regimes, from non-stiff to highly oscillatory. Thanks to an averaging transformation, the stiffness of the problem is softened, allowing for standard schemes to retain their usual orders of convergence. Overall, high-order numerical approximations are obtained with errors and at a cost independent of the regime.
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ISSN:1615-3375
1615-3383
DOI:10.1007/s10208-019-09413-3