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Some solutions of the linear and nonlinear Klein-Gordon equations using the optimal homotopy asymptotic method. (English) Zbl 1193.35190
Summary: We investigate the effectiveness of the Optimal Homotopy Asymptotic Method (OHAM) in solving time dependent partial differential equations. For this, we consider the homogeneous, non-homogeneous, linear and nonlinear Klein-Gordon equations with boundary conditions. The results reveal that the method is explicit, effective, and easy to use.

35Q53KdV-like (Korteweg-de Vries) equations
35A35Theoretical approximation to solutions of PDE
35A30Geometric theory for PDE, characteristics, transformations
Full Text: DOI
[1] Caudrey, P. J.; Eilbeck, I. C.; Gibbon, J. D.: The sine-Gordon equation as a model classical field theories, Nuovo cimento 25, 497-511 (1975)
[2] Deeba, E. Y.; Khuri, S. A.: A decomposition method for solving the nonlinear Klein -- Gordon equation, Journal of computational physics 124, 442-448 (1996) · Zbl 0849.65073 · doi:10.1006/jcph.1996.0071
[3] El-Sayed, S. M.: The decomposition method for studying the Klein -- Gordon equation, Chaos, solitons & fractals 18, 1025-1030 (2001) · Zbl 1068.35069 · doi:10.1016/S0960-0779(02)00647-1
[4] Ganji, D. D.; Rafei, M.: Solitary wave solution for a generalized Hirota -- satsuma coupled KdV equation by homotopy perturbation method, Physics letters A 356, 131-137 (2006) · Zbl 1160.35517 · doi:10.1016/j.physleta.2006.03.039
[5] He, J. H.: An approximation sol. Technique depending upon an artificial parameter, Communications in nonlinear science and numerical simulation 3, 92-97 (1998)
[6] He, J. H.: Periodic solution and bifurcations of delay-differential equations, Physics letters A 347, No. 4 -- 6, 228-230 (2005) · Zbl 1195.34116 · doi:10.1016/j.physleta.2005.08.014
[7] Herişanu, Nicolae; Marinca, Vasile; Dordea, Toma; Madescu, Gheorghe: A new analytical approach to nonlinear vibration of an electrical machine, Proceedings of the romanian Academy, series A 9, No. 3, 229-236 (2008)
[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.; Chwang, A. T.: Application of homotopy analysis method in nonlinear oscillations, ASME journal applied mechanics 65, 914 (1998)
[10] Marinca, Vasile; Herişanu, Nicolae: Application of optimal homotopy asymptotic method for solving nonlinear equations arising in heat transfer, International communications in heat and mass transfer 35, 710-715 (2008)
[11] Marinca, Vasile; Herişanu, Nicolae; Bota, Constantin; Marinca, Bogdan: An optimal homotopy asymptotic method applied to the steady flow of a fourth-grade fluid past a porous plate, Applied mathematics letters 22, 245-251 (2009) · Zbl 1163.76318
[12] Marinca, Vasile; Herişanu, Nicolae; Nemeş, Iacob: Optimal homotopy asymptotic method with application to thin film flow, Central European journal of physics 6, No. 3, 648-653 (2008)
[13] Siddiqui, A. M.; Irum, S.; 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, No. 4, 565-576 (2008) · Zbl 1156.76062 · doi:10.3846/1392-6292.2008.13.565-576
[14] Wazwaz, A. M.: The modified decomposition method for analytic treatment of differential equations, Applied mathematics and computation 173, 165-176 (2006) · Zbl 1089.65112 · doi:10.1016/j.amc.2005.02.048
[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, 1179-1195 (2005) · Zbl 1082.65584 · doi:10.1016/j.amc.2004.08.006