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A Developed New Algorithm for Evaluating Adomian Polynomials

M. Azreg-AÔnou
Journal / Anthology

Computer Modeling in Engineering & Sciences
Year: 2009
Volume: 42
Issue: 1
Page range: 1-18

Adomian polynomials (APís) are expressed in terms of new objects called reduced polynomials (RPís). These new objects, which carry two subscripts, are independent of the form of the nonlinear operator. Apart from the well-known two properties of APís, curiously enough no further properties are discussed in the literature. We derive and discuss in full detail the properties of the RPís and APís. We focus on the case where the nonlinear operator depends on one variable and construct the most general analytical expressions of the RPís for small values of the difference of their subscripts. It is shown that each RP depends on a number of functions equal to the difference of its subscripts plus one. These new properties lead to implement a dramatically simple and compact Mathematica program for the derivation of individual RPís and APís in their general forms and provide useful hints for elegant hand calculations of APís. Application of the program is considered.


Adomian decomposition method, Adomian polynomials, diophantine, equations, Mathematica