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Convergence of the Adomian decomposition method for initial‐value problems
Author(s) -
Abdelrazec Ahmed,
Pelinovsky Dmitry
Publication year - 2011
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20549
Subject(s) - adomian decomposition method , mathematics , convergence (economics) , initial value problem , context (archaeology) , mathematical analysis , decomposition method (queueing theory) , nonlinear system , decomposition , partial differential equation , physics , paleontology , ecology , discrete mathematics , quantum mechanics , biology , economics , economic growth
We prove convergence of the Adomian decomposition method for an abstract initial‐value problem using the method of majorants from the Cauchy‐Kowalevskaya theorem for differential equations with analytic vector fields. Convergence rates of the Adomian method are investigated in the context of the nonlinear Schrödinger equation. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 749–766, 2011