The variational iteration method for studying the Klein-Gordon equation

Applied Mathematics Letters

Volumn 21, Issue 7, 2008, Pages 669-674

  Yusufoǧlu, Elcin ^a  

^a DUMLUPINAR UNIVERSITY   (Turkey)

Author keywords

Adomian's decomposition method; Correction functional; Klein Gordon equations; Lagrange multiplier; Variational iteration method

Indexed keywords

LAGRANGE MULTIPLIERS; LINEAR EQUATIONS; NONLINEAR EQUATIONS;

CORRECTION FUNCTIONAL; KLEIN-GORDON EQUATIONS;

ITERATIVE METHODS;

EID: 43549101930     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2007.07.023     Document Type: Article

References (26)

1. Ablowitz M.J., and Clarkson P.A. Solitons, Nonlinear Evolution Equations and Inverse Scattering Transform (1990), Cambridge University Press, Cambridge
2. He J.H. A new approach to nonlinear partial differential equations. Comm. Nonlinear Sci. Numer. Simul. 2 (1997) 230-235
3. He J.H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput. Methods Appl. Mech. Engrg. 167 (1998) 57-68
4. He J.H. Approximate solution of nonlinear differential equations with convolution product nonlinearities. Comput. Methods Appl. Mech. Engrg. 167 (1998) 69-73
5. He J.H. Variational iteration method-A kind of non-linear analytical technique: Some examples. Internat. J. Non-Linear Mech. 34 (1999) 699-708
6. He J.H. Variational iteration method for autonomous ordinary differential systems. Appl. Math. Comput. 114 (2000) 115-123
7. He J.H. Variational principle for some nonlinear partial differential equations with variable coefficients. Chaos Solitons Fractals 19 (2004) 847-851
8. Abdou M.A., and Soliman A.A. New applications of variational iteration method. Physica D 211 (2005) 1-8
9. Abdou M.A., and Soliman A.A. Variational iteration method for solving Burgers' and coupled Burgers' equations. J. Comput. Appl. Math. 181 (2005) 245-251
10. Momani S., and Abuasad S. Application of He's variational iteration method to Helmholtz equation. Chaos Solitons Fractals 27 (2006) 1119-1123
11. Odibat Z.M., and Momani S. Application of variational iteration method to nonlinear differential equations of fractional order. Internat. J. Nonlinear Sci. Numer. Simul 7 (2006) 27-34
12. He J.H. Some asymptotic methods for strongly nonlinear equations. Internat. J. Modern Phys. B 20 (2006) 1141-1199
13. Abulwafa E.M., Abdou M.A., and Mahmoud A.A. The solution of nonlinear coagulation problem with mass loss. Chaos Solitons Fractals 26 (2006) 313-330
14. Bildik N., and Konuralp A. The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations. Internat. J. Nonlinear Sci. Numer. Simul. 7 (2006) 65-70
15. Dodd R.K., Eilbeck I.C., Gibbon J.D., and Morris H.C. Solitons and Nonlinear Wave Equations (1982), Academic, London
16. Khaliq A.Q., Abukhodair B., Sheng Q., and Ismail M.S. A predictor-corrector scheme for sine-Gordon equation. Numer. Methods Partial Differential Equations 16 (2000) 133-146
17. Lynch M.A.M. Large amplitude instability in finite difference approximations to the Klein-Gordon equation. Appl. Numer. Math. 31 (1999) 173-182
18. Lu X., and Schmid R. Symplectic integration of sine-Gordon type systems. Math. Comput. Simulation 50 (1999) 255-263
19. Kaya D. An implementation of the ADM for generalized one-dimensional Klein-Gordon equation. Appl. Math. Comput. 166 (2005) 426-433
20. Kaya D., and El-Sayed S.M. A numerical solution of the Klein-Gordon equation and convergence of the decomposition method. Appl. Math. Comput. 156 (2004) 341-353
21. El-Sayed S.M. The decomposition method for studying the Klein-Gordon equation. Chaos Solitons Fractals 18 (2003) 1025-1030
22. Wazwaz A.M. The modified decomposition method for analytic treatment of differential equations. Appl. Math. Comput. 173 (2006) 165-176
23. Adomian G. Solving Frontier Problems of Physics: The Decomposition Methods (1994), Kluwer Academic Publishers, Boston
24. Wazwaz A.M. A reliable modification of Adomian decomposition method. Appl. Math. Comput. 102 (1997) 77-86
25. Wazwaz A.M. A new algorithm for calculating Adomian polynomials for nonlinear operators. Appl. Math. Comput. 111 (2000) 53-69
26. Zhao X., Zhi H., Yu Y., and Zhang H. A new Riccati equation expansion method with symbolic computation to construct new travelling wave solution of nonlinear differential equations. Appl. Math. Comput. 172 (2006) 24-39