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An efficient algorithm for the multivariable Adomian polynomials. (English) Zbl 1204.65022
The Adomian decomposition methods are efficient techniques for solving nonlinear functional equations. This problem appears in coupled nonlinear differential equations $$Lu+Ru+Nu=g(t)$$, where $$L+R$$ is the linear part and $$N$$ is a nonlinear operator. The method consists in the decomposition of $$Nu=f(u)$$ in the series of Adomian polynomials $$A_n=\frac{1}{n!}\frac{d^n}{d\lambda_n}[f(\sum^\infty_{n=0}u_n\lambda^n)]_{\lambda=0}$$ depending of certain initial solutions $$u_i$$. The author gives an algorithm for rapid generation of the multivariable polynomials in question and tests it with a MATHEMATICA program.

##### MSC:
 65D20 Computation of special functions and constants, construction of tables 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 34A34 Nonlinear ordinary differential equations and systems, general theory 65L05 Numerical methods for initial value problems 12Y05 Computational aspects of field theory and polynomials (MSC2010)
Mathematica
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