International Scientific Journal


A meshless method based upon radial basis function is utilized to approximate the singularly perturbed Burgers-Huxley equation with the viscosity coefficient ε. The proposed method shows that the obtained solutions are reliable and accurate. Convergence analysis of method was analyzed in a numerical way for different small values of singularity parameter.
PAPER REVISED: 2016-05-07
PAPER ACCEPTED: 2016-05-09
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  1. Kyrychko. Y.N., et al., Persistence of traveling wave solution of a fourth order diffusion system, J. Comput. Appl. Math., 176 (2005), pp. 433-443.
  2. Loskutov. A.Y., Mikhailov. A.S., Introduction to Synergetics, Nauka, Moscow, 1990.
  3. Farrel. P.A., et al., Robust computational techniques for boundary layers, Chapman & Hall, London, 2000.
  4. Miller. J.J.H., et al., Fitted numerical methods for singular perturbation problems, World-Scientific, Singapore, 1996.
  5. Roos. H.G., et al., Numerical methods for singularly perturbed differential equations: convectio ndiffusion and flow problems, Springer-Verlag, Berlin, 1996.
  6. Molabahrami. A., Khani. F., The homotopy analysis method to solve the Burgers-Huxley equation equation, Nonlinear Anal. Real., 10 (2009), pp. 589-600.
  7. Deng. X., Travelling wave solutions for the generalized Burgers-Huxley equation, Appl. Math. Comput.204 (2008), pp. 733-737.
  8. Batiha. B., et al., Application of variational iteration method to the generalized Burgers-Huxley equation, Chaos Soliton Fract., 36 (2008), pp. 660-663.
  9. Liu. J., et al., New Multi-Soliton solitions for generalized Burgers-Huxley equation, Thermal Science., 17 (2013), pp. 1486-1489.
  10. Wazwaz. A.M., Analytic study on Burgers, Fisher, Huxley equations and combined forms of these equations, Appl. Math. Comput., 195 (2008), pp. 754-761.
  11. Wang. X.Y., et al., Solitary wave solutions of the generalized Burger's-Huxley equation, J. Phys. A: Math. Gen., 23 (1990), pp. 271-274.
  12. Liu. J., et al., New multi-Soliton solutions for generalized Burgers-Huxley equation, Thermal Science, 17 (2013), pp. 1486-1489.
  13. Javidi. M., A numerical solution of the generalized Burger's-Huxley equation by pseudospectral method and Darvishi's preconditioning, Appl. Math. Comput., 175 (2006), pp. 1619-1628.
  14. Khattak. A.J., A computational meshless method for the generalized Burger's-Huxley equation, Appl. Math. Model., 33 (2009), pp. 3718-3729.
  15. Rathish Kumar. B.V., et al., A numerical study of singularly perturbed generalized Burgers-Huxley equation using three-step Taylor-Galerkin method, Comput. Math. Appl., 62 (2011), pp. 776-786.
  16. Xie. H., Li. D., A meshless method for Burgers equation using MQ-RBF and high-order temporal approximation, Appl. Math. Model., 37 (2013), pp. 9215-9222.
  17. Roohani Ghehsareh. H., et al., A meshfree method based on the radial basis functions for solution of two-dimensional fractional evolution equation, Eng. Anal. Bound. Elem., 61 (2015), pp. 52-60.
  18. Shivanian. E., Spectral meshless radial point interpolation (SMRPI) method to two-dimensional fractional telegraph equation, Math. Meth. Appl. Sci., 39 (2016), pp. 1820-1835.
  19. Shivanian. E., et al., Meshless local radial point interpolation to three-dimensional wave equation with Neumann's boundary conditions, Inter. J. Comput. Math. doi: 10.1080/00207160.2015.1085032.
  20. Abbasbandy. S., et al., A meshfree method for the solution of two-dimensional cubic nonlinear Schrödinger equation, Eng. Anal. Bound. Elem., 37 (2013), pp. 885-898.
  21. Hon. Y.-C., et al., Local radial basis function collocation method for solving thermo-driven fluid-flow problems with free surface, Eng. Anal. Bound. Elem., 57 (2015), pp. 2-8.
  22. Sileimani. S., et al., Meshless local RBF-DG for 2-D heat conduction: A comparative study, Thermal Science, 15 (2011), pp. S117-S121.
  23. Benton. E., Platzman. G.W., A table of solutions of the one-dimensional Burgers equations, Quart. Appl. Math., 30 (1972), pp. 195-212.
  24. Hassanein. I.A., et al., Forth-order finite difference method for solving Burgers equation, Appl. Math. Comput., 170 (2005), pp. 781-800.
  25. Kansa. E.J., Multiquadrics-a scattered data approximation scheme with applications to computational fluid dynamics-II. Solution to parabolic, hyperbolic and elliptic partial differential equations, Computers Math. Applic., 19 (1990), pp. 147-161.
  26. Hon. Y.C., Mao. X.Z., An efficient numerical scheme for Burgers-Huxley equation, Appl. Math. Comput., 95 (1998), pp. 37-50.
  27. Wang. X.Y., et al., Solitary wave solutions of the generalised Burger-Huxley equation, J. Phys. A Math. Gen., 23 (1990), pp. 271-274.
  28. Gupta. V., Kadalbajoo. M.K., A singular perturbation approach to solve Burgers-Huxley equation via monotone finite difference scheme on layer-adaptive mesh, Commun Nonlinear Sci Numer Simulat., 16 (2011), pp. 1825-1844.

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