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Numerical resolution of linear evolution multidimensional problems of second order in time

โœ Scribed by B. Bujanda; J. C. Jorge; M. J. Moreta

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
264 KB
Volume
28
Category
Article
ISSN
0749-159X

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โœฆ Synopsis

Abstract

We present a new class of efficient time integrators for solving linear evolution multidimensional problems of secondโ€order in time named Fractional Step Rungeโ€Kuttaโ€Nystrรถm methods (FSRKN). We show that these methods, combined with suitable spliting of the space differential operator and adequate space discretizations provide important advantages from the computational point of view, mainly parallelization facilities and reduction of computational complexity. In this article, we study in detail the consistency of such methods and we introduce an extension of the concept of Rโ€stability for Rungeโ€Kuttaโ€Nystrรถm methods. We also present some numerical experiments showing the unconditional convergence of a third order method of this class applied to resolve one Initial Boundary Value Problem of second order in time. ยฉ 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 597โ€“620, 2012

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