Rouhparvar, H. (2010). A numerical solution of Nagumo telegraph equation by Adomian decomposition method. Theory of Approximation and Applications, 6(2), 73-81.

H. Rouhparvar. "A numerical solution of Nagumo telegraph equation by Adomian decomposition method". Theory of Approximation and Applications, 6, 2, 2010, 73-81.

Rouhparvar, H. (2010). 'A numerical solution of Nagumo telegraph equation by Adomian decomposition method', Theory of Approximation and Applications, 6(2), pp. 73-81.

Rouhparvar, H. A numerical solution of Nagumo telegraph equation by Adomian decomposition method. Theory of Approximation and Applications, 2010; 6(2): 73-81.

A numerical solution of Nagumo telegraph equation by Adomian decomposition method

^{}Department of Mathematics, Islamic Azad University, Saveh-Branch, Saveh 39187/366, Iran.

Abstract

In this work, the solution of a boundary value problem is discussed via a semi analytical method. The purpose of the present paper is to inspect the application of the Adomian decomposition method for solving the Nagumo tele- graph equation. The numerical solution is obtained for some special cases so that demonstrate the validity of method.

References

[1] T. A. Abassy, Improved Adomian decomposition method, Comput. Math. Appl. 9 (2010), 42{54. [2] S. Abbasbandy, Soliton solutions for the Fitzhugh-Nagumo equation with the homotopy analysis method, Appl. Math. Model., 32 (2008), 2706{2714. [3] S. Abbasbandy, A Numerical solution of Blasius equation by Adomian's decom- position method and comparison with homotopy perturbation method, Chaos, Solitons and Fractals, 31 (2007), 257{260. [4] S. Abbasbandy, Improving Newton-Raphson method for nonlinear equations by modied Adomian decomposition method, Appl. Math. Comput. 145 (2004), 887{893. [5] S. Abbasbandy, M.T. Darvish, A numerical solution of Burger's equation by modied Adomian method, Appl. Math. Comput. 163 (2005), 1265{1272. [6] H.A. Abdusalam, E.S. Fahmy, Cross-diusional eect in a telegraph reaction diusion Lotka-Volterra two competitive system, Chaos, Solitons & Fractals, 18 (2003), 259{264. [7] H. A. Abdusalam, Analytic and approximate solutions for Nagumo telegraph reaction diusion equation, Appl. Math. Comput. 157 (2004), 515{522.

[8] G. Adomain, Solving frontier problems of physics: The decomposition method, Kluwer Academic Publishers, Boston, 1994. [9] G. Adomian, Nonlinear stochastic operator equations, Academic Press, 1986. [10] G. Adomian, A review of the decomposition method in applied mathematics, J. Math. Anal. Appl. 135 (1998), 501{544. [11] G. Adomian, Y. Charruault, Decomposition method-A new proof of convergency, Math. Comput. Model. 18 (1993), 103{106. [12] E. Ahmed, H. A. Abdusalam, E. S. Fahmy, On telegraph reaction diusion and coupled map lattice in some biological systems, Int. J. Mod. Phys C, 2 (2001), 717{723. [13] E. Babolian, J. Biazar, Solution of a system of nonlinear Volterra integral equa- tions by Adomian decomposition method, Far East J. Math. Sci. 2 (2000), 935{ 945. [14] E. Babolian, Sh. Javadi, H. Sadeghi, Restarted Adomian method for integral equations, Appl. Math. Comput. 153 (2004), 353{359. [15] S. A. El-Wakil, M. A. Abdou, New applications of Adomian decomposition method, Chaos, Solitons and Fractals 33 (2007), 513{522. [16] A. C. Metaxas, R. J. Meredith, Industrial microwave, heating, Peter Peregrinus, London, 1993. [17] N. Ngarhasts, B. Some, K. Abbaoui, Y. Cherruault, New numerical study of Adomian method applied to a diusion model, Kybernetes 31 (2002), 61{75. [18] W. Liu, E. Van Vleck, Turning points and traveling waves in FitzHugh-Nagumo type equations, J. Di. Eq. 2 (2006), 381{410. [19] G. Roussy, J. A. Pearcy, Foundations and industrial applications of microwaves and radio frequency elds, John Wiley, New York, 1995. [20] R. A. Van Gorder, K. Vajravelu, A variational formulation of the Nagumo reaction-diusion equation and the Nagumo telegraph equation, Nonlinear Anal- ysis: Real World Applications 4 (2010), 2957{2962. [21] A.W. Wazwaz, A reliable modication of Adomian decomposition method, Appl. Math. Comput. 102 (1999), 77{86. [22] A. M. Wazwaz, A new algorithm for calculating Adomian polynomials for non- linear operators, Appl. Math. Comput. 111 (2000), 53{69.