A New Efficient Method for Nonlinear Fisher-Type Equations

Laplace transform and new homotopy perturbation methods are adopted to study Fisher-type equations analytically. The solutions introduced in this study can be used to obtain the closed form of the solutions if they are required. The combined method needs less work in comparison with the other homotopy perturbation methods and decreases volume of calculations considerably. The method is tested on various examples, and results show that new method is more effective and convenient to use, and high accuracy of it is evident.

[1]  Ji-Huan He.  HOMOTOPY PERTURBATION METHOD FOR SOLVING BOUNDARY VALUE PROBLEMS , 2006 .

[2]  Ji-Huan He.  Application of homotopy perturbation method to nonlinear wave equations , 2005 .

[3]  Ji-Huan He,et al.  Recent development of the homotopy perturbation method , 2008 .

[4]  Jafar Biazar,et al.  Exact solutions for non-linear Schrödinger equations by He's homotopy perturbation method , 2007 .

[5]  Saeid Abbasbandy,et al.  Numerical solutions of the integral equations: Homotopy perturbation method and Adomian's decomposition method , 2006, Appl. Math. Comput..

[6]  Mark J. Ablowitz,et al.  Explicit solutions of Fisher's equation for a special wave speed , 1979 .

[7]  Saeid Abbasbandy,et al.  A numerical solution of Blasius equation by Adomian’s decomposition method and comparison with homotopy perturbation method , 2007 .

[8]  Ji-Huan He,et al.  Addendum:. New Interpretation of Homotopy Perturbation Method , 2006 .

[9]  Ji-Huan He.  A coupling method of a homotopy technique and a perturbation technique for non-linear problems , 2000 .

[10]  Ji-Huan He.  Homotopy perturbation technique , 1999 .

[11]  Qingbiao Wu,et al.  Three-Dimensional Flow Arising in the Long Porous Slider: An Analytic Solution , 2011 .

[12]  W. Malfliet.  Solitary wave solutions of nonlinear wave equations , 1992 .

[13]  E. Yusufoglu,et al.  Homotopy Perturbation Method for Solving a Nonlinear System of Second Order Boundary Value Problems , 2007 .

[14]  John J. Tyson,et al.  On Traveling Wave Solutions of Fisher's Equation in Two Spatial Dimensions , 1999, SIAM J. Appl. Math..

[15]  Davood Domiri Ganji,et al.  Application of homotopy perturbation method in nonlinear heat conduction and convection equations , 2007 .

[16]  X. Y. Wang,et al.  Exact and explicit solitary wave solutions for the generalised fisher equation , 1988 .

[17]  Abdul-Majid Wazwaz,et al.  An analytic study of Fisher's equation by using Adomian decomposition method , 2004, Appl. Math. Comput..

[18]  Ji-Huan He,et al.  The homotopy perturbation method for nonlinear oscillators with discontinuities , 2004, Appl. Math. Comput..

[19]  Turgut Özis,et al.  An analytical study for Fisher type equations by using homotopy perturbation method , 2010, Comput. Math. Appl..

[20]  Takuji Kawahara,et al.  Interactions of traveling fronts: an exact solution of a nonlinear diffusion equation , 1983 .

[21]  Jonathan A. Sherratt.  On the transition from initial data to travelling waves in the Fisher-KPP equation , 1998 .

[22]  Qi Wang.  Homotopy perturbation method for fractional KdV-Burgers equation , 2008 .

[23]  Ji-Huan He.  New interpretation of homotopy perturbation method , 2006 .

[24]  Hossein Aminikhah,et al.  An efficient method for quadratic Riccati differential equation , 2010 .

[25]  D. S. Jones,et al.  Differential Equations and Mathematical Biology , 1983 .

[26]  A. Yildirim,et al.  Exact solutions to the perturbed nonlinear Schr¨ odinger's equation with Kerr law nonlinearity by using the first integral method , 2011 .

[27]  D. Ganji.  The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer , 2006 .

[28]  Davood Domiri Ganji,et al.  Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations , 2007 .

[29]  Qingbiao Wu,et al.  A Series Solution of the Long Porous Slider , 2011 .

[30]  Ji-Huan He.  Limit cycle and bifurcation of nonlinear problems , 2005 .