Determination of the source parameter in a heat equation with a non-local boundary condition
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摘要
In this article we consider the inverse problem of identifying a time dependent unknown coefficient in a parabolic problem subject to initial and non-local boundary conditions along with an overspecified condition defined at a specific point in the spatial domain. Due to the non-local boundary condition, the system of linear equations resulting from the backward Euler approximation have a coefficient matrix that is a quasi-tridiagonal matrix. We consider an efficient method for solving the linear system and the predictor–corrector method for calculating the solution and updating the estimate of the unknown coefficient. Two model problems are solved to demonstrate the performance of the methods.
论文关键词:Heat equation,Inverse problem,Non-local boundary condition
论文评审过程:Received 1 November 2006, Revised 12 September 2007, Available online 13 November 2007.
论文官网地址:https://doi.org/10.1016/j.cam.2007.10.060