Results 21 to 30 of about 334 (167)
Modified variational iteration method for analytical solutions of nonlinear oscillators
Journal of Low Frequency Noise, Vibration and Active Control, 2019 The second-order nonlinear oscillators have rich dynamics. We proposed a novel analytical method based on both variational iteration method and Adomian method. The variational iteration method is used to establish an equivalent integral system.
Wei He, Hua Kong, Yan-Mei Qin
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Comparative study of Adomian decomposition method and Clique polynomial method
Partial Differential Equations in Applied Mathematics, 2022 This paper generated the novel approach called the Clique polynomial method (CPM) using the Clique polynomials raised in graph theory. Nonlinear initial value problems are converted into nonlinear algebraic equations by discretization with suitable grid ...
Kumbinarasaiah S, Mallanagoud Mulimani
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Results in Physics, 2020 A numerical inverse Laplace transform method is established using Bernoulli polynomials operational matrix of integration. The efficiency of the method is demonstrated through some standard nonlinear differential equations: Duffing equation, Van der Pol ...
Dimple Rani, Vinod Mishra
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A simple algorithm for calculating Adomian polynomials [PDF]
International Journal of Contemporary Mathematical Sciences, 2007 In this paper, we introduce a new Algorithm for calculating Adomian polynomials and present some example to show the simplicity of the new Algorithm. The new Algorithm requires less computations in comparison with the previous methods, and can be extended to calculate Adomian polynomials for nonlinear functional with several variables.
J. Biazar, S. M. Shafiof
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Adomian decomposition method by Gegenbauer and Jacobi polynomials
International Journal of Computer Mathematics, 2011 In this paper, orthogonal polynomials on [–1,1] interval are used to modify the Adomian decomposition method (ADM). Gegenbauer and Jacobi polynomials are employed to improve the ADM and compared with the method of using Chebyshev and Legendre polynomials.
Cenesiz, Yucel, Kurnaz, Aydin
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Measuring the Pollutants in a System of Three Interconnecting Lakes by the Semianalytical Method
Journal of Applied Mathematics, 2021 Pollution has become an intense danger to our environment. The lake pollution model is formulated into the three-dimensional system of differential equations with three instances of input.
Indranil Ghosh +3 more
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A Comparison between Adomian’s Polynomials and He’s Polynomials for Nonlinear Functional Equations [PDF]
Mathematical Problems in Engineering, 2013 We will compare the standard Adomian decomposition method and the homotopy perturbation method applied to obtain the solution of nonlinear functional equations. We prove analytically that the two methods are equivalent for solving nonlinear functional equations. In Ghorbani (2009), Ghorbani presented a new definition which he called as He’s polynomials.
Hossein Jafari +2 more
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Using a hybrid technique for the analytical solution of a coupled system of two-dimensional BurgerŠs equations [PDF]
Results in Nonlinear Analysis, 2018 Our aim in this paper is to investigate the analytical solutions of two dimensional non- linear system of Burger’s equations. We present two problems for the efficiency of the proposed hybrid techniques form by coupling Laplace transform with Adomian ...
Atta Ullah, Kamal Shah
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Abstract and Applied Analysis, 2014 We develop a method to obtain approximate solutions for nonlinear systems of Volterra integrodifferential equations with the help of Sumudu decomposition method (SDM).
Hassan Eltayeb +2 more
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Mathematics, 2019 This work deals with a new modified version of the Adomian-Rach decomposition method (MDM). The MDM is based on combining a series solution and decomposition method for solving nonlinear differential equations with Adomian polynomials for nonlinearities.
Emad A. Az-Zo’bi +2 more
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