El-Sayed, Salah M. The decomposition method for studying the Klein-Gordon equation. (English) Zbl 1068.35069 Chaos Solitons Fractals 18, No. 5, 1025-1030 (2003). Summary: We use Adomian’s decomposition method for solving linear and nonlinear Klein-Gordon and sine-Gordon equations. Analytic and numerical studies are presented. The obtained results show improvements over existing techniques. Cited in 62 Documents MSC: 35L70 Second-order nonlinear hyperbolic equations 35A25 Other special methods applied to PDEs PDF BibTeX XML Cite \textit{S. M. El-Sayed}, Chaos Solitons Fractals 18, No. 5, 1025--1030 (2003; Zbl 1068.35069) Full Text: DOI References: [1] Abbaoui, K.; Cherruault, Y.; Seng, V., Practical formulae for the calculus of multivariable Adomian polynomials, Math. Comput. Modell., 22, 89-93 (1995) · Zbl 0830.65010 [2] Adomian, G., Solving Frontier problems of physics: the decomposition method (1994), Kluwer: Kluwer Boston · Zbl 0802.65122 [3] Adomian, G., A review of the decomposition method and some recent results for nonlinear equation, Math. Comput. Modell., 13, 17-43 (1992) · Zbl 0713.65051 [4] Adomian, G.; Rach, R., Equality of partial solutions in the decomposition method for linear or nonlinear partial differential equations, Comput. Math. Appl., 19, 9-12 (1990) · Zbl 0702.35058 [5] Caudrey, P. J.; Eilbeck, I. C.; Gibbon, J. D., The sine-Gordon equation as a model classical field theory, Nuovo Cimento, 25, 497-511 (1975) [6] Cherruault, Y.; Adomian, G., Decomposition method: a new proof of convergence, Math. Comput. Modell., 8, 103-106 (1993) · Zbl 0805.65057 [7] Cherrualt, Y.; Saccamandi, G.; Some, B., New results for convergence of Adomian’s method applied to integral equations, Math. Comput. Modell., 16, 83-93 (1992) [8] Dodd, R. K.; Eilbeck, I. C.; Gibbon, J. D.; Morris, H. C., Solitons and nonlinear wave equations (1982), Academic: Academic London · Zbl 0496.35001 [9] Ismail, M. S.; Sarie, T., Spline difference method for solving Klein-Gordon equations, Dirasat, 14, 189-196 (1989) [10] Khaliq, A. Q.; Sheng, Q.; Ismail, M. S., A predictor-corrector scheme for sine-Gordon equation, Numer. Meth. Partial Differen. Equat., 16, 133-146 (2000) · Zbl 0951.65089 [11] Lynch, M. A.M., Large amplitude instability in finite difference approximations to the Klein-Gordon equation, Appl. Numer. Math., 31, 173-182 (1999) · Zbl 0937.65098 [12] Lu, X.; Schmid, R., Symplectic integration of sine-Gordon type systems, Math. Comput. Simul., 50, 255-263 (1999) [13] El-Sayed, S. M., The modified decomposition method for solving nonlinear algebraic equations, Appl. Math. Comput., 132, 589-597 (2002) · Zbl 1031.65067 [15] Wazwaz, A. M., A first course in integral equations (1997), World Scientific: World Scientific New Jersey [16] Wazwaz, A. M., A reliable modification of Adomian’s decomposition method, Appl. Math. Comput., 102, 77-86 (1999) · Zbl 0928.65083 [17] Wazwaz, A. M., Analytical approximations and Pade’ approximants for Volterra’s population model, Appl. Math. Comput., 100, 13-35 (1999) · Zbl 0953.92026 [18] Wazwaz, A. M., A new approach to the nonlinear advection problem: an application of the decomposition method, Appl. Math. Comput., 72, 175-181 (1995) · Zbl 0838.65092 [19] Wazwaz, A. M., A new algorithm for calculating Adomian polynomials for nonlinear operators, Appl. Math. Comput., 111, 33-51 (2001) [20] Wazwaz, A. M.; El-Sayed, S. M., A new modification of Adomian decomposition method for linear and nonlinear operators, Appl. Math. Comput., 122, 393-405 (2001) · Zbl 1027.35008 [21] Wazwaz, A. M., Partial differential equations: methods and applications (2002), Balkema Publishers: Balkema Publishers The Netherlands · Zbl 0997.35083 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.