title: Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.
abstract: 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.
authors: Department of Electronic Engineering, Faculty of Engineering and Technology, International Islamic University, Islamabad, Pakistan.
authors: Suheel Abdullah
authors: SA
authors: Malik
authors: Department of Electrical Engineering, Air University, Islamabad, Pakistan.
authors: Ijaz Mansoor
authors: IM
authors: Qureshi
authors: Department of Electronic Engineering, Faculty of Engineering and Technology, International Islamic University, Islamabad, Pakistan.
authors: Muhammad
authors: M
authors: Amir
authors: Department of Electronic Engineering, Faculty of Engineering and Technology, International Islamic University, Islamabad, Pakistan.
authors: Aqdas Naveed
authors: AN
authors: Malik
authors: Department of Electronic Engineering, Faculty of Engineering and Technology, International Islamic University, Islamabad, Pakistan.
authors: Ihsanul
authors: I
authors: Haq
mesh_terms: D000465:Algorithms; D000066506:Heuristics; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted; D013997:Time Factors