A numerical solution of Nagumo telegraph equation by Adomian decomposition method

Theory of Approximation and Applications

مقاله 8، دوره 6، شماره 2، اسفند 2012، صفحه 73-81   

نوع مقاله: Research Articles

نویسنده

H. Rouhparvar^*

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

چکیده

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.

مراجع

[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
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{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 modication 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.