• Explicit symplectic multidimen...

Result: Explicit symplectic multidimensional exponential fitting modified Runge-Kutta-Nyström methods

Title:
Explicit symplectic multidimensional exponential fitting modified Runge-Kutta-Nyström methods
Authors:
XINYUAN WU, BIN WANG, JIANLIN XIA
Source:
BIT (Nordisk Tidskrift for Informationsbehandling). 52(3):773-795
Publisher Information:
Dordrecht: Springer, 2012.
Publication Year:
2012
Physical Description:
print, 29 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Equations différentielles, Ordinary differential equations, Probabilités et statistiques numériques, Numerical methods in probability and statistics, Ajustement, Fitting, Ajuste, Analyse numérique, Numerical analysis, Análisis numérico, Equation différentielle, Differential equation, Ecuación diferencial, Equation ordre 2, Second order equation, Ecuación orden 2, Extrapolation, Extrapolación, Matrice définie positive, Positive definite matrix, Matriz definida positiva, Matrice symétrique, Symmetric matrix, Matriz simétrica, Méthode Runge Kutta, Runge Kutta method, Método Runge Kutta, Méthode multipas, Multistep method, Método multipaso, Méthode numérique, Numerical method, Método numérico, Méthode stochastique, Stochastic method, Método estocástico, Système hamiltonien, Hamiltonian system, Sistema hamiltoniano, 37Jxx, 65C20, 65K15, 65L06, 65L05, 65M20, ERKN integrators, Exponential fitting, MEFMRKN methods, Oscillatory systems, Symplecticity conditions
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics, Nanjing University, Nanjing 210093, China
State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing 210093, China
Department of Mathematics, Purdue University, West Lafayette, IN 47907, United States
ISSN:
0006-3835
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=26309631
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.26309631
Database:
PASCAL Archive

Further Information

This paper is concerned with multidimensional exponential fitting modified Runge-Kutta-Nyström (MEFMRKN) methods for the system of oscillatory second-order differential equations q(t) + Mq(t) = f(q(t)), where M is a d x d symmetric and positive semi-definite matrix and f (q) is the negative gradient of a potential scalar U(q). We formulate MEFMRKN methods and show clearly the relationship between MEFMRKN methods and multidimensional extended Runge-Kutta-Nystrom (ERKN) methods proposed by Wu et al. (Comput. Phys. Comm. 181:1955―1962, 2010). Taking into account the fact that the oscillatory system is a separable Hamiltonian system with Hamiltonian H(p, q) = 1/2 pT p + 1/2qT Mq + U(q), we derive the symplecticity conditions for the MEFMRKN methods. Two explicit symplectic MEFMRKN methods are proposed. Numerical experiments accompanied demonstrate that our explicit symplectic MEFMRKN methods are more efficient than some well-known numerical methods appeared in the scientific literature.