A numerical solution of Nagumo telegraph equation by Adomian decomposition method

Document Type: Research Articles


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


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
telegraph equation. The numerical solution is obtained for some special cases
so that demonstrate the validity of method.

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
decomposition 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 modi ed Adomian decomposition method, Appl. Math.
Comput. 145 (2004), 887{893.
[5] S. Abbasbandy, M.T. Darvish, A numerical solution of Burger's equation
by modi ed Adomian method, Appl. Math. Comput. 163 (2005), 1265{
[6] H.A. Abdusalam, E.S. Fahmy, Cross-di usional e ect in a telegraph
reaction di usion Lotka-Volterra two competitive system, Chaos, Solitons
& Fractals, 18 (2003), 259{264.
[7] H. A. Abdusalam, Analytic and approximate solutions for Nagumo
telegraph reaction di usion equation, Appl. Math. Comput. 157 (2004),
[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,
[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 di usion
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
equations 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 di usion model, Kybernetes 31 (2002),
[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-di usion equation and the Nagumo telegraph equation, Nonlinear
Analysis: Real World Applications 4 (2010), 2957{2962.