A numerical solution of the Klein-Gordon equation and convergence of the decomposition method

Applied Mathematics and Computation

Volumn 156, Issue 2, 2004, Pages 341-353

  Kaya, Doǧan ^a   El Sayed, Salah M ^b,c  

^a FIRAT UNIVERSITY   (Turkey)

^b BENHA UNIVERSITY   (Egypt)

^c Girls College of Education Riyadh   (Saudi Arabia)

Author keywords

Convergence of the decomposition method; Decomposition method; Modified decomposition method; Nonlinear Klein Gordon equations

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; FINITE DIFFERENCE METHOD; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; PROBLEM SOLVING;

CONVERGENCE OF DECOMPOSITION METHODS; DECOMPOSITION METHODS; MODIFIED DECOMPOSITION METHODS; NONLINEAR KLEIN GORDON EQUATIONS;

DIFFERENTIAL EQUATIONS;

EID: 3943090453     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2003.07.014     Document Type: Article

References (21)

1. Adomian G. Solving Frontier Problems of Physics: The Decomposition Method. 1994;Kluwer Academic Publishers, Boston, MA.
2. Adomian G. A review of the decomposition method in applied mathematics. J. Math. Anal. Appl. 135:1988;501-544.
3. Jiminez B.S., Vazquez L. Analysis of four numerical schemes for a nonlinear Klein-Gordon equation. Appl. Math. Comput. 35:1990;61-94.
4. Ben-Yu G., Xun L., Vazquez L. A Legendre spectral method for solving the nonlinear Klein-Gordon equation. Comput. Appl. Math. 15:1996;19-36.
5. Li X., Guo B.Y. A Legendre spectral method for solving the nonlinear Klein-Gordon equation. J. Comput. Math. 15:1997;105-126.
6. Vu-Quoc L., Li S. Invariant-conserving finite difference algorithms for the nonlinear Klein-Gordon equation. Comput. Methods Appl. Mech. Engrg. 107:1993;314-391.
7. Wong Y.S., Chang Q., Gong L. An initial-boundary value problem of a nonlinear Klein-Gordon equation. Appl. Math. Comput. 84:1997;77-93.
8. Lynch M.A.M. Large amplitude instability in finite difference approximations to the Klein-Gordon equation. Appl. Numer. Math. 31:1999;173-182.
9. Ablowitz M.J., Herbst B.M., Schober C.M. Numerical simulation of quasi-periodic solutions of the sine-Gordon equation. Physica D. 87:1995;37-47.
10. Khaliq A.Q.M., Abukhoider B., Sheng Q., Ismail M.S. A predictor-corrector scheme for the sine-Gordon equation. Numer. Methods Partial Diff. Equat.: Int. J. 16:2000;133-146.
11. Argyris J., Haase M., Heinrich J.C. Finite element approximations to the two-dimensional sine-Gordon solutions. Comput. Methods Appl. Mech. Engrg. 86:1991;1-26.
12. D. Kaya, A closed form solution technique for solving nonlinear Klein-Gordon equations, in: Proceeding of the First International Conference on Nonlinear Analysis Nonlinear Modeling, 2001, pp. 28-36.
13. El-Sayed S.M. The decomposition method for studying the Klein-Gordon equation. Chaos Solitons Fractals. 18:2003;1025-1030.
14. D. Kaya, A numerical solution of the sine-Gordon equation using the modified decomposition method, Appl. Math. Comput., in press.
15. Drazin P.G., Johnson R.S. Solutions: An Introduction. 1989;Cambridge University Press, Cambridge.
16. Cherruault Y. Convergence of Adomian's method. Kybernetes. 18:1989;31-38.
17. Rèpaci A. Nonlinear dynamical systems: On the accuracy of Adomian's decomposition method. Appl. Math. Lett. 3:1990;35-39.
18. Cherruault Y., Adomian G. Decomposition methods: A new proof of convergence. Math. Comput. Model. 18:1993;103-106.
19. Ngarhasta N., Some B., Abbaoui K., Cherruault Y. New numerical study of Adomian method applied to a diffusion model. Kybernetes. 31:2002;61-75.
20. Mavoungou T., Cherruault Y. Convergence of Adomian's method and applications to nonlinear partial differential equations. Kybernetes. 21:1992;13-25.
21. Elwakil S.A., El-Labany S.K., Zahran M.A., Sabry R. Modified extended tanh-function method for solving nonlinear partial differential equations. Phys. Lett. A. 299:2002;179-188.