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A numerical study of parabolic problems with nonlinear boundary conditions
Author(s) -
Zolfaghari R.,
Shidfar A.
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2534
Subject(s) - mathematics , sinc function , nonlinear system , mathematical analysis , boundary value problem , convolution (computer science) , integral equation , algebraic equation , volterra integral equation , function (biology) , physics , quantum mechanics , machine learning , evolutionary biology , artificial neural network , computer science , biology
In this paper, we consider an initial‐boundary value problem for a parabolic equation with nonlinear boundary conditions. The solution to the problem can be expressed as a convolution integral of a Green's function and two unknown functions. We change the problem to a system of two nonlinear Volterra integral equations of convolution type. By using an explicit procedure on the basis of Sinc‐function properties, the resulting integral equations are replaced by a system of nonlinear algebraic equations, whose solution yields an accurate approximate solution to the parabolic problem. Some examples are considered to illustrate the ability of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.