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

✍ Scribed by Hina Khan; Shi-Jun Liao; R.N. Mohapatra; K. Vajravelu

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 211 KB
• Volume: 14
• Category: Article
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2008.11.003

✦ Synopsis

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.