Some solutions of the linear and nonlinear Klein-Gordon equations using the optimal homotopy asymptotic method

Applied Mathematics and Computation

Volumn 216, Issue 10, 2010, Pages 2898-2909

  Iqbal, S ^a   Idrees, M ^b   Siddiqui, A M ^c   Ansari, A R ^d  

^a PAKISTAN INSTITUTE OF NUCLEAR SCIENCE AND TECHNOLOGY   (Pakistan)

^b GIK INSTITUTE OF ENGINEERING SCIENCES AND TECHNOLOGY   (Pakistan)

^c PENNSYLVANIA STATE UNIVERSITY   (United States)

^d GULF UNIVERSITY FOR SCIENCE AND TECHNOLOGY   (Kuwait)

Author keywords

Klein Gordon equations; Optimal homotopy asymptotic method; Partial differential equations

Indexed keywords

KLEIN-GORDON EQUATION; NON-HOMOGENEOUS; NONLINEAR KLEIN-GORDON EQUATION; OPTIMAL HOMOTOPY ASYMPTOTIC METHOD; OPTIMAL HOMOTOPY ASYMPTOTIC METHODS; TIME-DEPENDENT PARTIAL DIFFERENTIAL EQUATIONS;

ASYMPTOTIC ANALYSIS; BOUNDARY CONDITIONS; COMPUTATIONAL FLUID DYNAMICS; OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS;

NONLINEAR EQUATIONS;

EID: 77953297512     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.04.001     Document Type: Article

References (15)

1. Caudrey P.J., Eilbeck I.C., and Gibbon J.D. The sine-Gordon equation as a model classical field theories. Nuovo Cimento 25 (1975) 497-511
2. Deeba E.Y., and Khuri S.A. A decomposition method for solving the nonlinear Klein-Gordon equation. Journal of Computational Physics 124 (1996) 442-448
3. El-Sayed S.M. The decomposition method for studying the Klein-Gordon equation. Chaos, Solitons & Fractals 18 (2001) 1025-1030
4. Ganji D.D., and Rafei M. Solitary wave solution for a generalized Hirota-Satsuma coupled kdv equation by homotopy perturbation method. Physics Letters A 356 (2006) 131-137
5. He J.H. An approximation sol. technique depending upon an artificial parameter. Communications in Nonlinear Science and Numerical Simulation 3 (1998) 92-97
6. He J.H. Periodic solution and bifurcations of delay-differential equations. Physics Letters A 347 4-6 (2005) 228-230
7. Herişanu N., Marinca V., Dordea T., and Madescu G. A new analytical approach to nonlinear vibration of an electrical machine. Proceedings of the Romanian Academy, Series A 9 3 (2008) 229-236
8. S.J. Liao, On the Proposed Homotopy Analysis Technique for Nonlinear Problems and its Applications, Ph.D. Dissertation, Shanghai Jio Tong University, Shanghai, China, 1992.
9. Liao S.J., and Chwang A.T. Application of homotopy analysis method in nonlinear oscillations. ASME Journal Applied Mechanics 65 (1998) 914
10. Marinca V., and Herişanu N. Application of optimal homotopy asymptotic method for solving nonlinear equations arising in heat transfer. International Communications in Heat and Mass Transfer 35 (2008) 710-715
11. Marinca V., Herişanu N., Bota C., and Marinca B. An optimal homotopy asymptotic method applied to the steady flow of a fourth-grade fluid past a porous plate. Applied Mathematics Letters 22 (2009) 245-251
12. Marinca V., Herişanu N., and Nemeş I. Optimal homotopy asymptotic method with application to thin film flow. Central European Journal of Physics 6 3 (2008) 648-653
13. Siddiqui A.M., Irum S., and Ansari A.R. A solution of the unsteady squeezing flow of a viscous fluid between parallel plates using the homotopy perturbation method. Journal of Mathematical Modelling and Analysis 13 4 (2008) 565-576
14. Wazwaz A.M. The modified decomposition method for analytic treatment of differential equations. Applied Mathematics and Computation 173 (2006) 165-176
15. Wazwaz A.M. The tanh and the sine-cosine methods for compact and noncompact solutions of the nonlinear Klein-Gordon equation. Applied Mathematics and Computation 167 (2005) 1179-1195