An Improved Algorithm for the Solution of Generalized Burger-Fishers Equation

Morufu Oyedunsi Olayiwola

Department of Mathematical and Physical Sciences, Faculty of Basic & Applied Sciences, College of Science, Engineering & Technology, Osun State University, Osogbo, Nigeria.

DOI: 10.4236/am.2014.510154                

Abstract

In this paper, an improved algorithm for the solution of Generalized Burger-Fisher’s Equation is presented. A Maple code is generated for the algorithm and simulated. It was observed that the algorithm gives the solution with less computation. The solution gives a better result when compared with the numerical solutions in the existing literature.

Keywords

Algorithm, PDE, MVIM, Generalized Burger-Fisher’s Equation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Goyal, A., Alka, R.G. and Kumar, C.N. (2011) Solitary Wave Solutions for Burgers-Fisher type Equations with Variable Coefficients. WASET, 60, 1742-1746.
[2]	Kaya, D. and El-Sayed, S.M. (2004) A Numerical Simulation and Explicit Solutions of the Generalized Berger-Fisher Equation. Applied Mathematics and Computation, 152, 403-413. http://dx.doi.org/10.1016/S0096-3003(03)00565-4
[3]	Ismail, H.N.A., Raslam, K. and Abd Rabboh, A.A. (2004) Adomian Decomposition Method for Generalized Burger’s-Huxley and Burger’s-Fisher Equation. Applied Mathematics and Computation, 159, 291-301. http://dx.doi.org/10.1016/j.amc.2003.10.050
[4]	He, J.-H. (2000) Variational Iteration Method for Autonomous Ordinary Differential System. Applied Mathematics and Computation, 114, 115-123. http://dx.doi.org/10.1016/S0096-3003(99)00104-6
[5]	He, J.-H. (1999) Variational Iteration Method—A Kind of Non-Linear Analytical Technique: Some Examples. International Journal of Non-Linear Mechanics, 34, 699-708. http://dx.doi.org/10.1016/S0020-7462(98)00048-1
[6]	He, J.-H. (1998) Approximate Analytical Solution for Seepage Flow with Fractional Derivatives in Porous Media. Computer Methods in Applied Mechanics and Engineering, 167, 57-68. http://dx.doi.org/10.1016/S0045-7825(98)00108-X
[7]	He, J.-H. (1998) Approximate Solution of Nonlinear Differential Equations with Convolution Product Nonlinearities. Computer Methods in Applied Mechanics and Engineering, 167, 69-73. http://dx.doi.org/10.1016/S0045-7825(98)00109-1
[8]	Ismail, H.N.A. and Rabboh, A.A.A. (2004) A Restrictive Pade Approximation for the Solution of the Generalized Fisher and Berger-Fisher Equation. Applied Mathematics and Computation, 154, 203-210. http://dx.doi.org/10.1016/S0096-3003(03)00703-3
[9]	Inokuti, M. (1978) General Use of the Lagrange Multiplier in Nonlinear Mathematical Physics. In: Nemat Nasser, S., Ed., Variational Method in the Mechanics of Solid, Pergamon Press, Oxford, 156-162.
[10]	Javidi, M. (2006) Modified Pseudospectral Method for generalized Burger’s-Fisher Equation. International Mathematical Forum, 1, 1555-1564.
[11]	Olayiwola, M.O., Gbolagade, A.W. and Akinpelu, F.O. (2011) An Efficient Algorithm for Solving the Nonlinear PDE. International Journal of Scientific and Engineering Research, 2, 1-10.
[12]	Olayiwola, M.O., Gbolagade, A.W. and Adesanya, A.O. (2010) An Efficient Algorithm for Solving the Telegraph Equation. Journal of the Nigerian Association of Mathematical Physics, 16, 199-204.
[13]	Olayiwola, M.O., Gbolagade, A.W. and Adesanya, A.O. (2010) Solving Variable Coefficient Fourth-Order Parabolic Equation by Modified initial guess Variational Iteration Method. Journal of the Nigerian Association of Mathematical Physics, 16, 205-210.
[14]	Olayiwola, M.O., Akinpelu, F.O. and Gbolagade, A.W. (2012) Modified Variational Iteration Method for the Solution of a Class of Differential Equations. American Journal of Computational and Applied Mathematics, 2, 228-231. http://dx.doi.org/10.5923/j.ajcam.20120205.05