Numerical treatment of oscillatory functional differential equations

In this paper we are concerned with oscillatory functional differential equations (that is, those equations where all the solutions oscillate) under a numerical approximation. Our interest is in the preservation of qualitative properties of solutions under a numerical discretisation. We give conditi...

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Vydané v:	Journal of computational and applied mathematics Ročník 234; číslo 9; s. 2757 - 2767
Hlavní autori:	Ford, Neville J., Yan, Yubin, Abdul Malique, Md
Médium:	Journal Article Konferenčný príspevok..
Jazyk:	English
Vydavateľské údaje:	Kidlington Elsevier B.V 01.09.2010 Elsevier
Predmet:	Approximation Computation Delay equations Difference and functional equations, recurrence relations Differential equations Discrete equations Exact sciences and technology Finite differences and functional equations Functional differential equations Mathematical analysis Mathematical models Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical approximation Numerical schemes Ordinary differential equations Oscillatory solutions Preservation Sciences and techniques of general use Discrete equations 39A12 65Q05 Delay equations Oscillatory solutions Functional differential equations Numerical schemes 34K11 Transcendental equation Oscillatory solution Differential equation Recurrence relation Functional equation Numerical method Difference equation Delay equation Discrete scheme Numerical approximation Numerical analysis Applied mathematics Numerical solution
ISSN:	0377-0427, 1879-1778
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Popis
Shrnutí:	In this paper we are concerned with oscillatory functional differential equations (that is, those equations where all the solutions oscillate) under a numerical approximation. Our interest is in the preservation of qualitative properties of solutions under a numerical discretisation. We give conditions under which an equation is oscillatory, and consider whether the discrete schemes derived using linear ϑ -methods will also be oscillatory. We conclude with some general theory.
Bibliografia:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0377-0427 1879-1778
DOI:	10.1016/j.cam.2010.01.035