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Solution of a semilinear parabolic equation with an unknown control function using the decomposition procedure of Adomian
Author(s) -
Dehghan Mehdi,
Tatari Mehdi
Publication year - 2007
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.20186
Subject(s) - adomian decomposition method , mathematics , partial differential equation , decomposition method (queueing theory) , parabolic partial differential equation , boundary value problem , mathematical analysis , series (stratigraphy) , domain (mathematical analysis) , power series , decomposition , boundary (topology) , function (biology) , domain decomposition methods , finite element method , paleontology , ecology , discrete mathematics , evolutionary biology , biology , physics , thermodynamics
The investigation of nonclassical parabolic initial‐boundary value problems, which involve an integral over the spatial domain of a function of the desired solution, is of considerable concern. In this article a parabolic partial differential equation subject to energy overspecification is studied. This problem is appeared in modeling of many physical phenomena. The Adomian decomposition method, which is an efficient method for solving various class of problems, is employed for solving this model. This method provides an analytical solution in terms of an infinite convergent power series. Some examples are reported to support the simplicity of the decomposition procedure of Adomian. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007