an:02173395
Zbl 1069.65104
Dehghan, Mehdi
Identification of a time-dependent coefficient in a partial differential equation subject to an extra measurement
EN
Numer. Methods Partial Differ. Equations 21, No. 3, 611-622 (2005).
00115713
2005
j
65M32 65M06 35K05 35R30
finite difference methods; conductivity of a medium; determination of a time-dependent coefficient; overspecified data; inverse problem; heat equation; numerical experiments
Summary: 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 experiments on several test problems.