Determination of a control function in three-dimensional parabolic equations

Mehdi Dehghan

Mathematics and Computers in Simulation (MATCOM), 2003, vol. 61, issue 2, 89-100

Abstract: This study presents numerical schemes for solving two three-dimensional parabolic inverse problems. These schemes are developed for indentifying the parameter p(t) which satisfy ut=uxx+uyy+uzz+p(t)u+φ, in R×(0,T], u(x,y,z,0)=f(x,y,z),(x,y,z)∈R=[0,1]3. It is assumed that u is known on the boundary of R and subject to the integral overspecification over a portion of the spatial domain ∫01∫01∫01u(x,y,z,t)dxdydz=E(t), 0≤t≤T, or to the overspecification at a point in the spatial domain u(x0,y0,z0,t)=E(t), 0≤t≤T, where E(t) is known and (x0,y0,z0) is a given point of R. These schemes are considered for determining the control parameter which produces, at any given time, a desired energy distribution in the spacial domain, or a desired temperature distribution at a given point in the spacial domain. A generalization of the well-known, explicit Euler finite difference technique is used to compute the solution. This method has second-order accuracy with respect to the space variables. The results of numerical experiments are presented and the accuracy and the central processor (CPU) times needed are reported.

Keywords: Parabolic partial differential equations; Inverse problem; Finite difference schemes; Explicit techniques; Overspecification; Source control parameters (search for similar items in EconPapers)
Date: 2003
References: View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:61:y:2003:i:2:p:89-100

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