On A Perturbation Method for Weakly Nonlinear Delay Differential Equations
Nikenasih Binatari, Wim van Horssen, Pieter Verstraten, Fajar Adi-Kusumo, and Lina Aryati

Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia

Department of Mathematics Education, Faculty of Mathematics and Natural Science, Universitas Negeri Yogyakarta, Yogyakarta, Indonesia

Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

Abstract

This research presents a new perturbation approach to study delay differential equations (DDE) including infinitely many eigenvalues related to the linear DDE. The existing perturbation methods approximate the solution of the O(1)-DDE only with a finite number of eigenvalues, [1-7]. Eliminating many eigenvalues could also eliminate the possibility of secular terms occurring in the approximations due to internal resonances. The solution of the linear DDE at the O(1)-level is obtained by using the Laplace transform method. We also present comparisons of the results which are obtained from the proposed analytical, the existing method and a numerical method. By considering all the eigenvalues, it is shown that the proposed method gives much better approximations on a long timescale.

Keywords: Delay Differential Equations, Perturbation Methods, Multiple time-scales

Topic: Minisymposia Differential Equations