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Abdou, M.A. and Soliman, A.A. (2005) Numerical Solutions of Nonlinear Evolution Equations Using Variational Iteration Method. Journal of Computational and Applied Mathematics, 207, 111-120.
https://doi.org/10.1016/j.cam.2006.07.016

has been cited by the following article:

• TITLE: Numerical Discrete-Domain Integral Formulations for Generalized Burger-Fisher Equation

  AUTHORS: Okey Oseloka Onyejekwe, Beruk Minale, Fikru Habtamu, Tesfaye Amha, Getenet Tamiru, Bethelhem Mengistu, Yohaness Demiss, Nahom Alemseged, Computational Science and Dynamics Systems Group

  KEYWORDS: Burger-Fisher Equation, Domain Integrals, Boundary Element, Finite-Element-Type Discrete Domain, Boundary Integral, Numerical, Nonlinearity

  JOURNAL NAME: Applied Mathematics, Vol.11 No.3, March 5, 2020

  ABSTRACT: In this study we use a boundary integral element-based numerical technique to solve the generalized Burger-Fisher equation. The essential feature of this method is the fundamental integral representation of the solution inside the problem domain by means of both the boundary and domain values. The occurrences of domain integrals within the problem arising from nonlinearity as well as the temporal derivative are not avoided or transferred to the boundary. However, unlike the classical boundary element approach, they are resolved within a finite-element-type discrete domain. The utility and correctness of this formulation are proved by comparing the results obtained herein with closed form solutions.