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A convergence analysis of the Adomian decomposition method for an abstract Cauchy problem of a system of first-order nonlinear differential equations
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A convergence analysis of the Adomian decomposition method for an abstract Cauchy problem of a system of first-order nonlinear differential equations

Lazhar Bougoffa, Randolph C. Rach and Said El-Manouni
International journal of computer mathematics, Vol.90(2), pp.360-375
01/02/2013
DOI: https://doi.org/10.1080/00207160.2012.718073

Abstract

Adomian decomposition method Adomian polynomials coupled system of nonlinear first-order differential equations
In this article, we study some fundamental results concerning the convergence of the Adomian decomposition method (ADM) for an abstract Cauchy problem of a system of first-order nonlinear differential equations. Under certain conditions, we obtain upper estimates for the norm of solutions of this system. We also obtain results about the error estimates for the approximate solutions by the ADM and discuss their applications.

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