An analytical solution for a nonlinear time-delay model in biology
Abbreviated Journal Title
Commun. Nonlinear Sci. Numer. Simul.
Time-delay; Series solution; Homotopy analysis method; EQUATIONS; FLUID; FLOW; Mathematics, Applied; Mathematics, Interdisciplinary Applications; Mechanics; Physics, Fluids & Plasmas; Physics, Mathematical
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.
Communications in Nonlinear Science and Numerical Simulation
"An analytical solution for a nonlinear time-delay model in biology" (2009). Faculty Bibliography 2000s. 1722.