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Identification of a time‐dependent coefficient in a partial differential equation subject to an extra measurement
Author(s) -
Dehghan Mehdi
Publication year - 2005
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.20055
Subject(s) - mathematics , first order partial differential equation , partial differential equation , partial derivative , parabolic partial differential equation , mathematical analysis , function (biology) , boundary value problem , identification (biology) , boundary (topology) , differential equation , botany , evolutionary biology , biology
The problem of recovering a time‐dependent coefficient in a parabolic partial differential equation has attracted considerable recent attention. Several finite difference schemes are presented for identifying the function u ( x , t ) and the unknown coefficient a ( t ) in a one‐dimensional partial differential equation. These schemes are developed to determine the unknown properties in a region by measuring only data on the boundary. Our goal has been focused on coefficients that presents physical quantities, for example, the conductivity of a medium. For the convenience of discussion, we will present the results of numerical experiment on several test problems. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005