Numerical treatment of oscillatory functional differential equations

Authors:
Neville J. Ford;Yubin Yan;Md. Abdul Malique
Affiliations:
Department of Mathematics, University of Chester, CH1 4BJ, United Kingdom;Department of Mathematics, University of Chester, CH1 4BJ, United Kingdom;Department of Mathematics, University of Chester, CH1 4BJ, United Kingdom
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

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 @q-methods will also be oscillatory. We conclude with some general theory.