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

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.

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.

Cite this paper

Olayiwola, M. (2014) An Improved Algorithm for the Solution of Generalized Burger-Fishers Equation.*Applied Mathematics*, **5**, 1609-1614. doi: 10.4236/am.2014.510154.

Olayiwola, M. (2014) An Improved Algorithm for the Solution of Generalized Burger-Fishers Equation.

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

[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