An Inverse Diffusion-Wave Problem Defined in Heterogeneous Medium with Additional Boundary Measurement

Authors : Nouiri BRAHİM, Djerioui KHAYRA

Pages : 16-21

View : 37 | Download : 13

Publication Date : 2019-06-15

Article Type : Conference Paper

Abstract :This paper deals with an inverse problem to determine a space-dependent coefficient in a one-dimensional time fractional diffusion-wave equation defined in heterogeneous medium with additional boundary measurement. Then, we construct the explicit finite difference scheme for the direct problem based on the equivalent partial integro-differential equation and Simpson`s rule. Using the matrix analysis and mathematical induction,  we prove that our scheme is stable and convergent . The least squares method with homotopy regularization is introduced to determine the space-dependent coefficient, and an inversion algorithm is performed by one numerical example. This inversion algorithm is effective at least for this inverse problem.
Keywords : Inverse problem, time fractional diffusion wave equation, Finite difference method

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