Solving delay differential equations with homotopy analysis method

Abstract

Delay differential equations have a wide range of application in science and engineering. They arise when the rate of change of a time-dependent process in its mathematical modeling is not only determined by its present state but also by a certain past state.In this paper, a nonlinear delay differential equation in biology was investigated. The approximation solution for the model was obtained by homotopy analysis method. 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. Compared with the numerical solution, the approximation solution has higher precision. It is showed that the homotopy analysis method was valid and feasible to the study of delay differential equations. © 2010 Springer-Verlag.