Convergence of Adomian's method applied to nonlinear equations
K. Abbaoui,Yves Cherruault +1 more
TLDR
In this paper, the authors give a proof of Adomian's method using only some properties of the nonlinear function, and apply these results to some concrete problems, such as the problem of finding a nonlinear solution to a set of nonlinear problems.About:
This article is published in Mathematical and Computer Modelling.The article was published on 1994-11-01 and is currently open access. It has received 233 citations till now. The article focuses on the topics: Adomian decomposition method & Numerical analysis.read more
Citations
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Viscous flow and heat transfer over a nonlinearly stretching sheet
TL;DR: This paper presents a numerical analysis for flow and heat transfer in a viscous fluid over a nonlinear stretching sheet by employing a novel numerical procedure that converts governing partial differential equations into highly nonlinear ordinary differential equations by a similarity transformation.
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Improving Newton-Raphson method for nonlinear equations by modified Adomian decomposition method
TL;DR: The modified Adomian decomposition method is applied to construct the numerical algorithms based on Newton-Raphson method and some numerical illustrations are given to show the efficiency of algorithms.
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Iterative methods improving newton's method by the decomposition method
TL;DR: In this paper, a sequence of iterative methods improving Newton's method for solving nonlinear equations is presented, and the order of convergence is derived analytically, and then rederived by applying symbolic computation of Maple.
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Peristaltic flow of viscoelastic fluid with fractional Maxwell model through a channel
TL;DR: The paper presents the transportation of viscoelastic fluid with fractional Maxwell model by peristalsis through a channel under long wavelength and low Reynolds number approximations.
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A new analytic algorithm of Lane-Emden type equations
TL;DR: An reliable, ease-to-use analytic algorithm is provided for Lane-Emden type equation which models many phenomena in mathematical physics and astrophysics and provides a convenient way to adjust convergence regions even without Pade technique.
References
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Decomposition methods: A new proof of convergence
Y. Cherruault,George Adomian +1 more
TL;DR: In this paper, a new convergence proof of Adomian's technique based on properties of convergent series is proposed, and the authors deduce some results about the speed of convergence of this method allowing us to solve nonlinear functional equations.
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Convergence of Adomian's method applied to differential equations
K. Abbaoui,Yves Cherruault +1 more
TL;DR: In this paper, a new proof of convergence of Adomian's method applied to differential equations is presented, along with new formulae and properties, and a simple computational form for adomian polynomials.
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New ideas for proving convergence of decomposition methods
K. Abbaoui,Yves Cherruault +1 more
TL;DR: In this article, the authors give new formulae which calculate easily the Adomian's polynomials used in decomposition methods, and prove the convergence of the technique using a weak hypothesis on the nonlinear operator of the functional equation.
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Algebraic computation and the decomposition method
George Adomian,Randolph Rach +1 more
TL;DR: The decomposition method of Adomian has recently been generalized in a number of directions and is now applicable to wide classes of linear and nonlinear, deterministic and stochastic differential, partial differential, and differential delay equations as well as algebraic equations of all types including polynomial equations, matrix equations, equations with negative or nonintegral powers, and random algebraic expressions.