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

    Authors

    H. Khan; S. J. Liao; R. N. Mohapatra;K. Vajravelu

    Abbreviated Journal Title

    Commun. Nonlinear Sci. Numer. Simul.

    Keywords

    Time-delay; Series solution; Homotopy analysis method; EQUATIONS; FLUID; FLOW; Mathematics, Applied; Mathematics, Interdisciplinary Applications; Mechanics; Physics, Fluids & Plasmas; Physics, Mathematical

    Abstract

    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.

    Journal Title

    Communications in Nonlinear Science and Numerical Simulation

    Volume

    14

    Issue/Number

    7

    Publication Date

    1-1-2009

    Document Type

    Article

    Language

    English

    First Page

    3141

    Last Page

    3148

    WOS Identifier

    WOS:000264147400031

    ISSN

    1007-5704

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