An algorithm for the systematic construction of solutions to perturbed problems

DOI10.1016/S0010-4655(98)00037-XzbMath0931.65072OpenAlexW1966956478MaRDI QIDQ1299704

Pablo Martín, José-Miguel Farto, Ana-Belén González

Publication date: 6 December 1999

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0010-4655(98)00037-x

zbMATH Keywords

performancealgorithmNewton polygonDuffing oscillatorcomputer algebraMaple V packagevan der Pol equationtruncated solutionperturbed differential equation

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Complexity and performance of numerical algorithms (65Y20) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Packaged methods for numerical algorithms (65Y15)

Related Items

An explicit Numerov-type method for second-order differential equations with oscillating solutions ⋮ A new pair of explicit ARKN methods for the numerical integration of general perturbed oscillators ⋮ New explicit adapted Numerov methods for second-order oscillatory differential equations ⋮ An adapted explicit hybrid method of Numerov-type for the numerical integration of perturbed oscillators ⋮ Trigonometrically-fitted Scheifele two-step methods for perturbed oscillators ⋮ Generalization of the Störmer method for perturbed oscillators without explicit first derivatives ⋮ A symplectic Runge-Kutta-Nyström method with minimal phase-lag ⋮ Scheifele two-step methods for perturbed oscillators ⋮ Legendre-Gauss collocation method for initial value problems of second order ordinary differential equations ⋮ Laguerre-Gauss collocation method for initial value problems of second order ODEs ⋮ On the numerical integration of oscillatory problems with multistep codes ⋮ An algorithm for an eigenvalues problem in the Earth rotation theory ⋮ Increasing the accuracy in the numerical integration of perturbed oscillators with new methods ⋮ New methods for oscillatory problems based on classical codes ⋮ A variable-stepsize variable-order multistep method for the integration of perturbed linear problems

Uses Software

• Maple

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On ODE-solver based on the method of averaging
• Nonlinear differential equations and dynamical systems
• An extension of the Newton-Puiseux polygon construction to give solutions of Pfaffian forms
• An algorithm for an eigenvalues problem in the Earth rotation theory
• Multiplicity of the solutions of a differential polynomial
• Multistep Numerical Methods Based on the Scheifele G-Functions with Application to Satellite Dynamics
• A transformation of the two-body problem
• A general canonical transformation increasing the number of variables with application to the two-body problem
• Power Series Expansions for the Frequency and Period of the Limit Cycle of the Van Der Pol Equation
• Le mouvement Keplerien et les oscillateurs harmoniques.

This page was built for publication: An algorithm for the systematic construction of solutions to perturbed problems