Result: EFFICIENT COMPUTATION OF DELAY DIFFERENTIAL EQUATIONS WITH HIGHLY OSCILLATORY TERMS
Title:
EFFICIENT COMPUTATION OF DELAY DIFFERENTIAL EQUATIONS WITH HIGHLY OSCILLATORY TERMS
Source:
Modélisation mathématique et analyse numérique (Imprimé). 46(6):1407-1420
Publisher Information:
Les Ulis: EDP Sciences, 2012.
Publication Year:
2012
Physical Description:
print, 12 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Mechanics acoustics, Mécanique et acoustique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Equations différentielles, Ordinary differential equations, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Equations algébriques et transcendantes non linéaires, Nonlinear algebraic and transcendental equations, Probabilités et statistiques numériques, Numerical methods in probability and statistics, Analyse numérique, Numerical analysis, Análisis numérico, Développement asymptotique, Asymptotic expansion, Desarrollo asintótico, Equation algébrique, Algebraic equation, Ecuación algebraica, Equation différentielle, Differential equation, Ecuación diferencial, Equation non linéaire, Non linear equation, Ecuación no lineal, Equation transcendante, Transcendental equation, Ecuación trascendente, Equation à retard, Delay equation, Ecuación retardada, Logiciel, Software, Logicial, Modèle mathématique, Mathematical model, Modelo matemático, Méthode numérique, Numerical method, Método numérico, Méthode stochastique, Stochastic method, Método estocástico, Oscillation, Oscilación, Raisonnement, Reasoning, Razonamiento, Résolution problème, Problem solving, Resolución problema, Solution asymptotique, Asymptotic solution, Solution numérique, Numerical solution, Système équation, Equation system, Sistema ecuación, 34XX, 65C20, 65H10, 65K15
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
School of Electronic Engineering, Dublin City University, Dublin 9, Ireland
Dpto. de Matemáticas, Universidad Carlos III de Madrid, Avda. Universidad, 30, Leganés 28911, Madrid, Spain
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Rd, CB3 OWA Cambridge, United Kingdom
Institute of Mathematics, University of Gdansk, Wit Stwosz Str. 57, 80-952 Gdansk, Poland
Dpto. de Matemáticas, Universidad Carlos III de Madrid, Avda. Universidad, 30, Leganés 28911, Madrid, Spain
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Rd, CB3 OWA Cambridge, United Kingdom
Institute of Mathematics, University of Gdansk, Wit Stwosz Str. 57, 80-952 Gdansk, Poland
ISSN:
0764-583X
Rights:
Copyright 2014 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
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.26721335
Database:
PASCAL Archive
Further Information
This paper is concerned with the asymptotic expansion and numerical solution of systems of linear delay differential equations with highly oscillatory forcing terms. The computation of such problems using standard numerical methods is exceedingly slow and inefficient, indeed standard software is practically useless for this purpose. We propose an alternative, consisting of an asymptotic expansion of the solution, where each term can be derived either by recursion or by solving a non-oscillatory problem. This leads to methods which, counter-intuitively to those developed according to standard numerical reasoning, exhibit improved performance with growing frequency of oscillation.