An analytical solution for a nonlinear time-delay model in biology

被引：36

作者：

Khan, Hina ^{[1
]}

Liao, Shi-Jun ^{[1
]}

Mohapatra, R. N. ^{[2
]}

Vajravelu, K. ^{[2
]}

机构：

[1] Shanghai Jiao Tong Univ, Sch Naval Architecture Ocean & Civil Engn, State Key Lab Ocean Engn, Shanghai 200240, Peoples R China

[2] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2009年 / 14卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Time-delay; Series solution; Homotopy analysis method; FLUID; FLOW;

D O I：

10.1016/j.cnsns.2008.11.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the homotopy analysis method is applied to develop a analytic approach for nonlinear differential equations with time-delay. A nonlinear model in biology is used as an example to show the basic ideas of this analytic approach. Different from other analytic techniques, the homotopy analysis method provides a simple way to ensure the convergence of the solution series, so that one can always get accurate approximations. A new discontinuous function is defined so as to express the piecewise continuous solutions of time-delay differential equations in a way convenient for symbolic computations. It is found that the time-delay has a great influence on the solution of the time-delay nonlinear differential equation. This approach has general meanings and can be applied to solve other nonlinear problems with time-delay. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：3141 / 3148

页数：8

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