Runge-Kutta projection methods with low dispersion and dissipation errors

Calvo, Manuel (Universidad de Zaragoza) ; Laburta, María Pilar (Universidad de Zaragoza) ; Montijano, Juan Ignacio (Universidad de Zaragoza) ; Rández, Luis (Universidad de Zaragoza)
Runge-Kutta projection methods with low dispersion and dissipation errors
Resumen: In this paper new one-step methods that combine Runge–Kutta (RK) formulae with a suitable projection after the step are proposed for the numerical solution of Initial Value Problems. The aim of this projection is to preserve some first integral in the numerical integration. In contrast with standard orthogonal projection, the direction of the projection at each step is obtained from another suitable embed- ded formula so that the overall method is affine invariant. A study of the local errors of these projection methods is carried out, showing that by choosing proper embedded formulae the order can be increased for the harmonic oscillator. Particular embedded formulae for the third order method by Bogacki and Shampine (BS3) are provided. Some criteria to get appropriate dynamical directions for general problems as well as sufficient conditions that ensure the existence of RK methods embedded in BS3 according to them are given. Finally, some numerical experiments to test the behaviour of the new projection methods are presented.
Idioma: Inglés
DOI: 10.1007/s10444-014-9355-2
Año: 2015
Publicado en: ADVANCES IN COMPUTATIONAL MATHEMATICS 41, 1 (2015), 231-251
ISSN: 1019-7168

Factor impacto JCR: 1.325 (2015)
Categ. JCR: MATHEMATICS, APPLIED rank: 56 / 254 = 0.22 (2015) - Q1 - T1
Factor impacto SCIMAGO: 1.007 - Computational Mathematics (Q2) - Applied Mathematics (Q2)

Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2010-21630-C02-01
Tipo y forma: Article (PostPrint)
Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)

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