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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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 234; no. 9; pp. 2757 - 2767
Main Authors: Ford, Neville J., Yan, Yubin, Abdul Malique, Md
Format: Journal Article Conference Proceeding
Language:English
Published: Kidlington Elsevier B.V 01.09.2010
Elsevier
Subjects:
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
Online Access:Get full text
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Summary: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.
Bibliography: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