Solving a Parabolic Inverse Source Problem by the Sinc-Galerkin Method
Keywords:
Nonhomogeneous parabolic equation, inverse problem, unknown source term, Sinc-Galerkin method, Neumann boundary conditionAbstract
In this paper, the inverse problem of determining an unknown source term in a parabolic equation with Neumann boundary conditions and final measured data is considered. Initially, the unknown source term is estimated in the form of a combination of orthogonal functions. Since this inverse problem is ill-posed, the Tikhonov regularization technique is applied to find a stable solution. Then, a Sinc-Galerkin system is assembled to solve the direct problem. The approximate solution displays an exponential convergence rate. At the end of the paper, the proposed method is tested on 2 examples.
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