Exponentially-fitted Runge-Kutta-Nyström method for the numerical solution of initial-value problems with oscillating solutions
type: Item
instance of: scholarly article
title: Exponentially-fitted Runge-Kutta-Nyström method for the numerical solution of initial-value problems with oscillating solutions
zbMATH Open document ID: 1003.65081
DOI: 10.1016/S0893-9659(01)00121-5
published in: Applied Mathematics Letters
publication date: 2002-08-15T00:00:00Z
review text: The author constructs effectively a new three stage Runge-Kutta-Nyström methods of order four for \[ {d^2u\over dt^2}= f(t, u(x)) \] provided that the solutions are periodic or oscillating. Stability is analyzed and numerical experiments are carried out.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1781881
zbMATH Keywords: periodic solution
zbMATH Keywords: oscillating solution
zbMATH Keywords: error bound
zbMATH Keywords: stability
zbMATH Keywords: Runge-Kutta-Nyström methods
zbMATH Keywords: numerical experiments
author: T. E. Simos
MaRDI profile type: Publication
cites work: Families of Runge-Kutta-Nystrom Formulae
cites work: Solving Ordinary Differential Equations I
cites work: Embedded methods for the numerical solution of the Schrödinger equation
cites work: On finite difference methods for the solution of the Schrödinger equation
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cites work: Symmetric linear multistep methods for second-order differential equations with periodic solutions
cites work: Chebyshevian multistep methods for ordinary differential equations
cites work: Stabilization of Cowell's method
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description: scientific article; zbMATH DE number 1781881