A convergence analysis of the ADM and an application

作者: Doǧan Kaya , Ibrahim E. Inan

DOI: 10.1016/J.AMC.2003.12.063

关键词: Convergence (routing)Decomposition (computer science)Korteweg–de Vries equationDecomposition method (constraint satisfaction)MathematicsInitial value problemVries equationAdomian decomposition methodMathematical analysis

摘要: In this paper by considering the decomposition scheme, we solve modified Korteweg-de Vries equation (MKdV for short) initial condition. We prove convergence of Adomian method (ADM) applied to MKdV equation.

参考文章(18)
N. Ngarhasta, B. Some, K. Abbaoui, Y. Cherruault, New numerical study of Adomian method applied to a diffusion model Kybernetes. ,vol. 31, pp. 61- 75 ,(2002) , 10.1108/03684920210413764
Luc Molinet, Francis Ribaud, On the Cauchy Problem for the Generalized Korteweg-de Vries Equation Pediatric Dermatology. ,vol. 28, pp. 2065- 2091 ,(2003) , 10.1081/PDE-120025496
G. Adomian, R. Rach, Noise terms in decomposition solution series Computers & Mathematics With Applications. ,vol. 24, pp. 61- 64 ,(1992) , 10.1016/0898-1221(92)90031-C
M. C. Shen, Asymptotic Theory of Unsteady Three-Dimensional Waves in a Channel of Arbitrary Cross Section SIAM Journal on Applied Mathematics. ,vol. 17, pp. 260- 271 ,(1969) , 10.1137/0117026
D. J. Korteweg, G. de Vries, XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves Philosophical Magazine Series 1. ,vol. 39, pp. 422- 443 ,(1895) , 10.1080/14786449508620739
G. B. Whitham, Richard G. Fowler, Linear and Nonlinear Waves ,(1974)
Dogan Kaya, Mohammed Aassila, An application for a generalized KdV equation by the decomposition method Physics Letters A. ,vol. 299, pp. 201- 206 ,(2002) , 10.1016/S0375-9601(02)00652-7
Abdul-Majid Wazwaz, Necessary conditions for the appearance of noise terms in decomposition solutions series Applied Mathematics and Computation. ,vol. 81, pp. 265- 274 ,(1997) , 10.1016/S0096-3003(95)00327-4
G Adomian, A review of the decomposition method in applied mathematics Journal of Mathematical Analysis and Applications. ,vol. 135, pp. 501- 544 ,(1988) , 10.1016/0022-247X(88)90170-9