Adomian Decomposition Method with Orthogonal Polynomials: Laguerre Polynomials and the Second Kind of Chebyshev Polynomials [PDF]
Mathematics, 2021 In this paper, a new efficient and practical modification of the Adomian decomposition method is proposed with Laguerre polynomials and the second kind of Chebyshev polynomials which has not been introduced in other articles to the best of our knowledge.
Yingying Xie, Lingfei Li
exaly +5 more sources
New recurrence algorithms for the nonclassic Adomian polynomials
Computers and Mathematics With Applications, 2011 In this article, we present new algorithms for the nonclassic Adomian polynomials, which are valuable for solving a wide range of nonlinear functional equations by the Adomian decomposition method, and introduce their symbolic implementation in ...
Jun-Sheng Duan
exaly +3 more sources
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.
Yücel Cenesiz
exaly +4 more sources
Mathematics, 2019 In this work, we applied the improved differential transform method to find the solutions of the systems of equations of Lane-Emden type arising in various physical models.
Lie-jun Xie, Cai-lian Zhou, Song Xu
doaj +2 more sources
Padé-Sumudu-Adomian Decomposition Method for Nonlinear Schrödinger Equation
Journal of Applied Mathematics, 2021 The main purpose of this paper is to solve the nonlinear Schrödinger equation using some suitable analytical and numerical methods such as Sumudu transform, Adomian Decomposition Method (ADM), and Padé approximation technique. In many literatures, we can
Metomou Richard, Weidong Zhao
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Analytic solutions for Euler–Bernoulli beams with axial compression resting on a nonlinear elastic foundation using MADM [PDF]
Scientific ReportsThis article investigates the deflection behavior of Euler–Bernoulli beams subjected to axial compression and resting on a nonlinear elastic foundation.
Li-Kuo Chou, Ming-Xian Lin
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Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods [PDF]
Journal of Applied Mathematics, 2014 The modified decomposition method (MDM) and homotopy perturbation method (HPM) are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis.
Norhasimah Mahiddin, S. A. Hashim Ali
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A novel technique using integral transforms and residual functions for nonlinear partial fractional differential equations involving Caputo derivatives. [PDF]
PLoS ONEFractional nonlinear partial differential equations are used in many scientific fields to model various processes, although most of these equations lack closed-form solutions.
Zareen A Khan +3 more
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Journal of Applied Mathematics, 2018 In this paper, we used Bernstein polynomials to modify the Adomian decomposition method which can be used to solve linear and nonlinear equations. This scheme is tested for four examples from ordinary and partial differential equations; furthermore, the ...
Ahmed Farooq Qasim, Ekhlass S. AL-Rawi
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MathematicsIn engineering, physics, and other fields, implicit ordinary differential equations are essential to simulate complex systems. However, because of their intrinsic nonlinearity and difficulty separating higher-order derivatives, implicit ordinary ...
Brahim Benhammouda, Hector Vazquez-Leal
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