A COMPARATIVE STUDY OF ADOMIAN DECOMPOSITION METHOD AND VARIATIONAL ITERATION METHOD
Keywords:
Adomian decomposition method (ADM), approximate Lagrange multipliers, exact Lagrange multipliers, variational iteration method (VIM).DOI:
https://doi.org/10.17654/2277141722009Abstract
In this paper, we present a comparative study between the variational iteration method and the Adomian decomposition method. The study highlights the significant features of both the methods. The analysis is illustrated by working out some problems on ordinary and partial differential equations.
Received: July 11, 2022
Received: August 29, 2022
Accepted: September 15, 2022
References
K. Abbaoui, Les fondements de la méthode décompositionnelle d’Adomian et application à la résolution de problèmes issus de la biologie et de la medicine, Thèse de Doctorat de l’Université Paris VI, 1995.
N. Ngarhasta, B. Some, K. Abbaoui and Y. Cherruault, New numerical study of Adomian method applied to a diffusion model, Kybernetes 31(1) (2002), 61-75.
Joseph Bonazebi Yindoula, Gabriel Bissanga, Pare Youssouf, Francis Bas-Sono and Blaise Some, Application of the Adomian Decomposition Method (ADM) and the decomposition Laplace-Adomian method to solving some equation of the models of water pollution, Advances in Dynamical Systems and Applications (ADSA) 10(1) (2015), 1-11.
S. Abbasbandy, A new application of He’s variational iteration method for quadratic Riccati differential equation by using Adomian’s polynomials, J. Comput. Appl. Math. 207 (2007), 59-63.
A. Mehmood, F. J. Awan and S. T. Mohyud-Din, Comparison of Lagrange multiplier for non-linear BVPs, International Journal of Modern Mathematical Science 5(3) (2003), 156-165.
A. Wazwaz, The variational iteration method for solving linear and nonlinear ODEs and scientific models with variable coefficients, Cent. Eur. J. Eng. 4(1) (2014), 64-71.
A. Wazwaz, Linear and Nonlinear Differential Equations, Methods and Applications, Higher Education Press, Beijing, Springer-Verleg, Heidelberg, 2011.
G. Wu, Challenge in the variational iteration method - a new approach to identification of the Lagrange multipliers, Journal of King Saud University Science 25 (2013), 175-178.
H. K. Dass, Advance engineering mathematics for the students of M.E, B.E and other Engineering Examination, S. Chand & Company Ltd, Ram Nagar, New Delhi, 2008.
N. H. Sweilam, Variational iteration method for solving cubic nonlinear Schrödinger equation, J. Comput. Appl. Math. 207 (2007), 155-163.
N. Bildik and A. Konuralp, Two-dimensional differential transform method, Adomian decomposition method, and variational iteration method for partial differential equations, Int. J. Comput. Math. 83 (2006), 973-987.
S. Abbasbandy, Numerical solutions of nonlinear Klein-Gordon equation by variational iteration method, Internat. J. Numer. Mech. Eng. 70 (2007), 876-881.
M. A. Abdou and A. A. Soliman, New applications of variational iteration method, Phys. D 211(1-2) (2005), 1-8.
J. H. He, Some asymptotic methods for strongly nonlinear equation, Int. J. Mod. Phys. 20(10) (2006), 1144-1199.
M. Inokuti, H. Sekine and T. Mura, General use of the Lagrange multiplier in nonlinear mathematical physics, Variational Method in the Mechanics of Solids, S. Nemat-Naseer, ed., Pergamon Press, New York, 1978, pp. 156-162.
S. T. Mohyud-Din, Modified variational iteration method for integro-differential equations and coupled systems, Z. Naturforsch. 65a (2010), 277-284.
J. I. Ramos, On the variational iteration method and other iterative techniques for nonlinear differential equations, Appl. Math. Comput. 199 (2008), 39-69.
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