A Jacobi-Gauss-Lobatto collocation method for solving generalized Fitzhugh-Nagumo equation with time-dependent coefficients

Applied Mathematics and Computation

Volumn 222, Issue , 2013, Pages 255-264

  Bhrawy, A H ^a,b  

^a KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^b Beni Suef University   (Egypt)

Author keywords

Collocation method; Generalized Fitzhugh Nagumo equation; Implicit Runge Kutta method; Jacobi Gauss Lobatto quadrature; Real Newell Whitehead equation; Time dependent Fitzhugh Nagumo equation

Indexed keywords

COLLOCATION METHOD; FITZHUGH-NAGUMO EQUATIONS; IMPLICIT RUNGE-KUTTA METHOD; JACOBI-GAUSS-LOBATTO QUADRATURE; NEWELL-WHITEHEAD EQUATION;

ORDINARY DIFFERENTIAL EQUATIONS; RUNGE KUTTA METHODS;

NUMERICAL METHODS;

EID: 84882382834     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2013.07.056     Document Type: Article

References (33)

1. S. Abbasbandy Soliton solutions for the Fitzhugh-Nagumo equation with the homotopy analysis method Appl. Math. Model. 32 2008 2706 2714
2. S. Abbasbandy, and E. Shivanian Multiple solutions of mixed convection in a porous medium on semi-infinite interval using pseudo-spectral collocation method Commun. Nonlinear Sci. Numer. Simul. 16 2011 2745 2752
3. H.A. Abdusalam Analytic and approximate solutions for Nagumo telegraph reaction diffusion equation Appl. Math. Comput. 157 2004 515 522
4. D.G. Aronson, and H.F. Weinberger Multidimensional nonlinear diffusion arising in population genetics Adv. Math. 30 1978 33 76
5. A.H. Bhrawy, and A.S. Alofi A Jacobi-Gauss collocation method for solving nonlinear Lane-Emden type equations Commun. Nonlinear. Sci. Numer. Simul. 17 2012 62 70
6. P. Browne, E. Momoniat, and F.M. Mahomed A generalized Fitzhugh-Nagumo equation Nonlinear Anal. 68 2008 1006 1015 (Pubitemid 350216263)
7. C. Canuto, M.Y. Hussaini, A. Quarteroni, and T.A. Zang Spectral Methods: Fundamentals in Single Domains 2006 Springer-Verlag New York
8. E.H. Doha, and A.H. Bhrawy Efficient spectral-Galerkin Algorithms for direct solution of fourth-order differential equations using Jacobi polynomials Appl. Numer. Math. 58 2008 1224 1244 (Pubitemid 351718463)
9. E.H. Doha, and A.H. Bhrawy A Jacobi spectral Galerkin method for the integrated forms of fourth-order elliptic differential equations Numer. Methods Partial Differ. Equ. 25 2009 712 739
10. E.H. Doha, A.H. Bhrawy, and S.S. Ezz-Eldien A new Jacobi operational matrix: an application for solving fractional differential equation Appl. Math. Model. 36 2012 4931 4943
11. E.H. Doha, A.H. Bhrawy, and R.M. Hafez A Jacobi-Jacobi dual-Petrov-Galerkin method for third- and fifth-order differential equations Math. Comput. Model. 53 2011 1820 1832
12. M. El-Kady Jacobi discrete approximation for solving optimal control problems J. Korean Math. Soc. 49 2012 99 112
13. R. Fitzhugh Impulse and physiological states in models of nerve membrane Biophys. J. 1 1961 445 466
14. B.-Y. Guo, and J.-P. Yan Legendre-Gauss collocation method for initial value problems of second order ordinary differential equations Appl. Numer. Math. 59 2009 1386 1408
15. G. Hariharan, and K. Kannan Haar Wavelet Method for Solving FitzHugh-Nagumo Equation vol. 67 2010 World Academy of Science, Engineering and Technology
16. A. Hajipour, and S.M. Mahmoudi Application of exp-function method to Fitzhugh-Nagumo equation World Appl. Sci. J. 9 2010 113 117
17. A.J.M. Jawad, M.D. Petkovic, and A. Biswas Modified simple equation method for nonlinear evolution equations Appl. Math. Comput. 217 2010 869 877
18. R. Jiwari A Haar wavelet quasilinearization approach for numerical simulation of Burgers' equation Comput. Phys. Commun. 183 2012 2413 2423
19. M. Kamrani, and S.M. Hosseini Spectral collocation method for stochastic Burgers equation driven by additive noise Math. Comput. Simul. 82 2012 1630 1644
20. T. Kawahara, and M. Tanaka Interactions of traveling fronts: an exact solution of a nonlinear diffusion equation Phys. Lett. 97A 1983 311 314
21. A.H. Khater, R.S. Temsah, and D.K. Callebaut Numerical solutions for some coupled nonlinear evolution equations by using spectral collocation method Math. Comput. Model. 48 2008 1237 1253
22. H. Li, and Y. Guo New exact solutions to the Fitzhugh-Nagumo equation Appl. Math. Comput. 180 2006 524 528 (Pubitemid 44441537)
23. R.C. Mittal, and R. Jiwari Numerical solution of two-dimensional reaction-diffusion Brusselator system Appl. Math. Comput. 217 2011 5404 5415
24. R.C. Mittal, and R. Jiwari A differential quadrature method for numerical solutions of Burgers'-type equations Int. J. Numer. Methods Heat Fluid Flow 22 2012 880 895
25. J.S. Nagumo, S. Arimoto, S. Yoshizawa, An active pulse transmission line simulating nerve axon, in: Proc. IRE, vol. 50, 1962, pp. 2061-2070.
26. M. Shih, E. Momoniat, and F.M. Mahomed Approximate conditional symmetries and approximate solutions of the perturbed Fitzhugh-Nagumo equation J. Math. Phys. 46 2005 023503
27. Y.-S. Sun, and B.-W. Li Chebyshev collocation spectral method for one-dimensional radiative heat transfer in graded index media Int. J. Thermal Sci. 48 2009 691 698
28. Y.-S. Sun, and B.-W. Li Chebyshev collocation spectral approach for combined radiation and conduction heat transfer in one-dimensional semitransparent medium with graded index Int. J. Heat Mass Transfer 53 2010 1491 1497
29. R.A. Van Gorder, and K. Vajravelu A variational formulation of the Nagumo reaction-diffusion equation and the Nagumo telegraph equation Nonlinear Anal. Real World Appl. 11 2010 2957 2962
30. R.A. Van Gorder Gaussian waves in the Fitzhugh-Nagumo equation demonstrate one role of the auxiliary function H (x, t) in the homotopy analysis method Commun. Nonlinear Sci. Numer. Simul. 17 2012 1233 1240
31. A.-M. Wazwaz The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations Appl. Math. Comput. 188 2007 1467 1475 (Pubitemid 46710038)
32. H. Triki, and A.-M. Wazwaz On soliton solutions for the Fitzhugh-Nagumo equation with time-dependent coefficients Appl. Math. Model. 37 2013 3821 3828
33. L. Zhu, and Q. Fan Solving fractional nonlinear Fredholm integro-differential equations by the second kind Chebyshev wavelet Commun. Nonlinear Sci. Numer. Simul. 17 2012 2333 2341