Results 1 to 10 of about 498,085 (213)
Simple Parametrization Methods for Generating Adomian Polynomials [PDF]
Applicable Analysis and Discrete Mathematics, 2016 In this paper, we discuss two simple parametrization methods for calculating Adomian polynomials for several nonlinear operators, which utilize the orthogonality of functions einx, where n is an integer.
Kataria, K. K., Vellaisamy, P.
core +5 more sources
A New Algorithm to Determine Adomian Polynomials for Nonlinear Polynomial Functions [PDF]
SSRN Electronic Journal, 2023 We present a new algorithm by which the Adomian polynomials can be determined for scalar-valued nonlinear polynomial functional in a Hilbert space. This algorithm calculates the Adomian polynomials without the complicated operations such as parametrization, expansion, regrouping, differentiation, etc. The algorithm involves only some matrix operations.
Mithun Bairagi
openaire +3 more sources
Correlation between Adomian and Partial Exponential Bell Polynomials [PDF]
Comptes Rendus. Mathématique, 2017 We obtain some recurrence relationships among the partition vectors of the partial exponential Bell polynomials. On using such results, the $n$-th Adomian polynomial for any nonlinear operator can be expressed explicitly in terms of the partial ...
Kataria, K. K., Vellaisamy, P.
core +6 more sources
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, Mancang Wang
doaj +2 more sources
Solution of nonlinear higher-index Hessenberg DAEs by Adomian polynomials and differential transform method. [PDF]
Springerplus, 2015 The solution of higher-index Hessenberg differential-algebraic equations (DAEs) is of great importance since this type of DAEs often arises in applications. Higher-index DAEs are known to be numerically and analytically difficult to solve. In this paper,
Benhammouda B.
europepmc +2 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
Numerical resolution of Emden's equation using Adomian polynomials [PDF]
International Journal of Numerical Methods for Heat & Fluid Flow, 2013 Purpose: In this paper the authors aim to show the advantages of using the decomposition method introduced by Adomian to solve Emden's equation, a classical non‐linear equation that appears in the study of the thermal behaviour of a spherical cloud and ...
Aznar Gregori, Fidel +4 more
core +5 more sources
Adomian polynomials method for dynamic equations on time scales
Advances in the Theory of Nonlinear Analysis and its Application, 2021 In a recent paper, a series solution method based on combining the Laplace transform and Adomian polynomial expansion was proposed to find an approximate solution of nonlinear differential equations \cite{FA2016}. It uses the expansion in Adomian polynomials defined in \cite {A1,A2}.
Svetlin GEORGİEV, İnci M. ERHAN
openaire +4 more sources
Iraqi Journal of PhysicsIn this study, one-dimensional non-linear Klein-Gordon equations are solved by applying the integral transform known as the Rohit transform method. The approximate solutions of one-dimensional non-linear Klein- Gordon equations are obtained by combining
Rohit Gupta, Rahul Gupta
doaj +2 more sources
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
doaj +2 more sources