Numerical solution of the inverse problem of determining an unknown source term in a two-dimensional heat equation Afet Golayoglu Fatullayev Baskent University, School of Applied Sciences, Baglica Kampus, Ankara, Turkey Abstract A numerical procedure for an inverse problem of determination of unknown source term in two-dimensional parabolic equation is presented. The approach of the proposed method is to approximate unknown function by a piecewise linear function whose co- efficients are determined from the solution of minimisation problem based on the overspecified data. Some numerical examples are presented. Ó 2003 Elsevier Inc. All rights reserved. Keywords: Parabolic equations; Inverse problems; Unknown source; Finite difference method; Overspecified data 1. Introduction In this paper we solve the problem of structural identification of an un- known source term in a two-dimensional heat equation from overspecified data measured on the boundary of the spatial region where the equation applies. This problem is described by the following inverse problem. Find uðx; y ; tÞ and F ðuÞ satisfy u t ðx; y ; tÞ¼ Duðx; y ; tÞþ F ðuðx; y ; tÞÞ ðx; y ; tÞ2 Q T ¼ X ð0; T  ð1Þ along with initial condition uðx; y ; 0Þ¼ u 0 ; ðx; y Þ2 X ð2Þ E-mail address: afet@baskent.edu.tr (A.G. Fatullayev). 0096-3003/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/S0096-3003(03)00582-4 Applied Mathematics and Computation 152 (2004) 659–666 www.elsevier.com/locate/amc