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Z. Naturforsch. 67a, 621 – 627
(2012)
doi:10.5560/ZNA.2012-0066
A Numerical Study of the Nonlinear Reaction-Diffusion Equation with Different Type of Absorbent Term by Homotopy Analysis Method
Department of Mathematics and Statistics, Center for Mathematical Sciences, Banasthali University, Banasthali – 304 022, India
Received April 17, 2012 / revised June 28, 2012 / published online September 19, 2012
Reprint requests to: P. K. G. ; E-mail:
praveen.rs.apm@itbhu.ac.in
In this paper, based on the homotopy analysis method (HAM), a new powerful algorithm is used for the solution of the nonlinear reaction-diffusion equation. The algorithm presents the procedure of constructing a set of base functions and gives the high-order deformation equation in a simple form. Different from all other analytic methods, it provides us with a simple way to adjust and control the convergence region of the solution series by introducing an auxiliary parameter h. The solutions of the problem of presence and absence of absorbent term and external force for different particular cases are presented graphically.
Key words: Homotopy Analysis Method; Nonlinear Reaction-Diffusion Equation; Partial Differential Equation; External Force; Reaction Term.
Mathematics Subject Classification 2000: 14F35; 35K57; 45K05