An implementation of the ADM for generalized one-dimensional Klein-Gordon equation

Applied Mathematics and Computation

Volumn 166, Issue 2, 2005, Pages 426-433

  Kaya, Doǧan ^a  

^a FIRAT UNIVERSITY   (Turkey)

Author keywords

Solitary wave solution; The decomposition method; The generalized one dimensional Klein Gordon equation; Traveling wave solution

Indexed keywords

APPROXIMATION THEORY; FUNCTIONS; PROBLEM SOLVING; WAVE EQUATIONS; WAVE PROPAGATION;

SOLITARY WAVE SOLUTION; THE DECOMPOSITION METHOD; THE GENERALIZED ONE-DIMENSIONAL KLEIN-GORDEN EQUATION; TRAVELING WAVE SOLUTION;

NONLINEAR EQUATIONS;

EID: 19944406452     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.06.103     Document Type: Article

References (29)

1. W. Zhang, Q. Chang, and E. Fan Methods of judging shape of solitary wave and solution formulae for some evolution equations with nonlinear terms of high order J. Math. Anal. Appl. 287 2003 118
2. P.A. Clarkson, R.J. LeVeque, and R. Saxton Solitary wave interactions in elastic rods Stud. Appl. Math. 75 1986 95 122
3. I.L. Bogolubsky Some examples of inelastic soliton interaction Comput. Phys. Commun. 13 1977 149 155
4. J. Li, and L. Zhang Bifurcations of traveling wave solutions in generalized one-dimensional Klein-Gordon equation Chaos Solitons and Fractal 14 2002 581 593
5. W. Zhang, and W. Ma Explicit solitary wave solutions to generalized one-dimensional Klein-Gordon Equations Appl. Math. Mech. 20 1999 666 674
6. G. Adomian Solving Frontier Problems of Physics: The Decomposition Method 1994 Kluwer Academic Publishers Boston
7. G. Adomian A review of the decomposition method in applied mathematics J. Math. Anal. Appl. 135 1988 501 544
8. A.M. Wazwaz A reliable modification of adomian decomposition method Appl. Math. Comp. 102 1999 77 86
9. A.M. Wazwaz Partial Differential Equations: Methods and Applications 2002 Balkema Publishers The Netherlands
10. V. Seng, K. Abbaoui, and Y. Cherruault Adomian's polynomials for nonlinear operators Math. Comput. Modell. 24 1996 59 65
11. Y. Cherruault Convergence of Adomian's method Kybernetes 18 1989 31 38
12. A. Répaci Nonlinear dynamical systems: on the accuracy of Adomian's decomposition method Appl. Math. Lett. 3 1990 35 39
13. Y. Cherruault, and G. Adomian Decomposition methods: a new proof of convergence Math. Comput. Model. 18 1993 103 106
14. K. Abbaoui, and Y. Cherruault Convergence of Adomian's method applied to differential equations Comput. Math. Appl. 28 1994 103 109
15. K. Abbaoui, and Y. Cherruault New ideas for proving convergence of decomposition methods Comput. Math. Appl. 29 1995 103 108
16. K. Abbaoui, M.J. Pujol, Y. Cherruault, N. Himoun, and P. Grimalt A new formulation of Adomian method: convergence result Kybernetes 30 2001 1183 1191
17. N. Shawagfeh Non perturbative approximate solution for Lane-Emden equation J. Math. Phys. 34 1993 4364 4369
18. G. Adomian, R. Rach, and N. Shawagfeh On the analytical solution of the Lane-Emden equation Found. Phys. Lett. 8 1995 161 181
19. D. Kaya On the solution of a Korteweg-de Vries like equation by the decomposition method Int. J. Comput. Math. 72 1999 531 539
20. D. Kaya An application of the decomposition method on second order wave equations Int. J. Comput. Math. 75 2000 235 245
21. D. Kaya, and M. Aassila An application for a generalized KdV equation by the decomposition method Phys. Lett. A 299 2002 201 206
22. D. Kaya A new approach to the telegraph equation: an application of the decomposition method Bull. Inst. Math. Acad. Sin. 28 2000 51 57
23. D. Kaya, and S.M. El-Sayed An application of the decomposition method for the generalized KdV and RLW equations Chaos, Solitons and Fractals 17 2003 869 877
24. D. Kaya, and S.M. El-Sayed On a generalized fifth order KdV equations Phys. Lett. A 310 2003 44 51
25. S.M. El-Sayed The decomposition method for studying the Klein-Gordon equation Chaos, Solitons & Fractals 18 2003 1025 1030
26. D. Kaya, and S.M. El-Sayed On the solution of the coupled Schrödinger-KdV equation by the decomposition method Phys. Lett. A 313 2003 82 88
27. D. Kaya, and S.M. El-Sayed Numerical soliton-like solutions of the potential Kadomstev-Petviashvili equation by decomposition method Phys. Lett. A 320 2003 192 199
28. D. Kaya A numerical simulation of solitary-wave solutions of the generalized regularized long-wave equation Appl. Math. Comput. 149 2004 833 841
29. S.M. El-Sayed, and D. Kaya Comparing numerical methods for Helmholtz equation model problem Appl. Math. Comput. 150 2004 763 773