Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substituti...

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Bibliographic Details
Published in:PloS one 2015-03, Vol.10 (3), p.e0121728-e0121728
Main Authors: Malik, Suheel Abdullah, Qureshi, Ijaz Mansoor, Amir, Muhammad, Malik, Aqdas Naveed, Haq, Ihsanul
Format: Article
Language:English
Subjects:
Algorithms
Applied mathematics
Asymptotic methods
Chromosomes
Fitness
Genetic algorithms
Heuristic methods
Heuristics
Hybridization
Mathematical programming
Methods
Models, Theoretical
Mutation
Nonlinear differential equations
Numerical Analysis, Computer-Assisted
Optimization
Parameter estimation
Partial differential equations
Perturbation methods
Queuing theory
Reproductive fitness
Time Factors
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Summary:In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0121728