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A numerical approximation to the solution of an inverse heat conduction problem
Author(s) -
Azari Hossein,
Zhang Shuhua
Publication year - 2010
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.20418
Subject(s) - mathematics , uniqueness , partial differential equation , inverse problem , heat equation , boundary value problem , backward euler method , euler's formula , convergence (economics) , mathematical analysis , parabolic partial differential equation , thermal conduction , variable (mathematics) , euler equations , thermodynamics , physics , economics , economic growth
The aim of this article is to study the parabolic inverse problem of determination of the leading coefficient in the heat equation with an extra condition at the terminal. After introducing a new variable, we reformulate the problem as a nonclassical parabolic equation along with the initial and boundary conditions. The uniqueness and continuous dependence of the solution upon the data are demonstrated, and then finite difference methods, backward Euler and Crank–Nicolson schemes are studied. The results of some numerical examples are presented to demonstrate the efficiency and the rapid convergence of the methods. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010