Simple Parametrization Methods for Generating Adomian Polynomials
Reads0
Chats0
TLDR
In this article, two simple parametrization methods for calculating Adomian polynomials for several nonlinear operators, which utilize the orthogonality of functions einx, where n is an integer.Abstract:
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. Some important
properties of Adomian polynomials are also discussed and illustrated with
examples. These methods require minimum computation, are easy to implement,
and are extended to multivariable case also. Examples of different forms of
nonlinearity, which includes the one involved in the Navier Stokes equation,
is considered. Explicit expression for the n-th order Adomian polynomials are
obtained in most of the examples.read more
Citations
More filters
Journal ArticleDOI
Cubic-quartic bright optical solitons with improved Adomian decomposition method
TL;DR: Graphical abstract Cubic-quartic soliton transmission having power law of nonlinearity refractive index having powerLaw of non linearityRefractive index.
Journal ArticleDOI
Saigo space–time fractional Poisson process via Adomian decomposition method
TL;DR: In this article, a generalization of the space-time fractional Poisson process involving the Caputo type Saigo differential operator is introduced and its state probabilities are obtained using ADM.
Journal ArticleDOI
Numerical solution for Triki-Biswas equation by Adomian decomposition method
TL;DR: In this article, the authors apply the Adomian decomposition method (ADM) to solve the Triki-Biswas equation for the special case of singular solitons when m = 2.
Sheffer and Brenke polynomials associated with generalized Bell numbers
TL;DR: In this paper, the first two authors have studied the integer number sequences generated by the higher order Bell polynomials, and they studied their basic properties and introduced new sequences of associated Sheffer and Brenke polynomial sequences.
Journal ArticleDOI
Correlation between Adomian and partial exponential Bell polynomials
TL;DR: In this article, the n -th Adomian polynomial for any nonlinear operator can be expressed explicitly in terms of the partial exponential Bell polynomials and some new identities are obtained by solving certain ordinary differential equations using the adomian decomposition method.
References
More filters
Journal ArticleDOI
A new algorithm for calculating adomian polynomials for nonlinear operators
TL;DR: A reliable technique for calculating Adomian polynomials for nonlinear operators will be developed and the algorithm will be illustrated by studying suitable forms of nonlinearity.
Book
Nonlinear Stochastic Systems Theory and Applications to Physics
TL;DR: In this paper, the authors present a decomposition method for differential and partial differential Equations of the An Polynomials for composite nonlinearity and linearization problems.
Journal ArticleDOI
A convenient computational form for the Adomian polynomials
TL;DR: In this article, simple symmetry rules are established to yield Adomian's polynomials quickly to high orders for nonlinear stochastic systems with nonlinearity dependent on the non-linearity.