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Duan, Jun-Sheng

An efficient algorithm for the multivariable Adomian polynomials. (English) Zbl 1204.65022

Appl. Math. Comput. 217, No. 6, 2456-2467 (2010).
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.
Reviewer: Jacek Gilewicz (Marseille)

Cited in 56 Documents

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
65L05 Numerical methods for initial value problems involving ordinary differential equations
12Y05 Computational aspects of field theory and polynomials (MSC2010)

Keywords:

Adomian decomposition method; nonlinear differential equation; multivariable function; algorithm; multivariable polynomials; MATHEMATICA program

Software:

Mathematica
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\textit{J.-S. Duan}, Appl. Math. Comput. 217, No. 6, 2456--2467 (2010; Zbl 1204.65022)
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References:

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