A new algorithm for calculating Adomian polynomials

摘要

In this paper, a new algorithm for calculating Adomian polynomials for nonlinear operators will be established by parametrization. The algorithm requires less formula than the previous method developed by Adomian [Nonlinear Stochastic Operator Equations, Academic Press, 1986, G. Adomian, R. Rach, On composite nonlinearities and decomposition method. J. Math. Anal. Appl. 113 (1986) 504–509, G. Adomian, Applications of Nonlinear Stochastic Systems Theory to Physics, Kluwer, 1988]. Many forms of nonlinearity will be studied to illustrate the new algorithm. The new algorithm will be extended to calculate Adomian polynomials for nonlinearity of several variables.