- Proceedings of International Mathematical Sciences
- Vol: 1 Issue: 1
- An Inverse Diffusion-Wave Problem Defined in Heterogeneous Medium with Additional Boundary Measureme...
An Inverse Diffusion-Wave Problem Defined in Heterogeneous Medium with Additional Boundary Measurement
Authors : Nouiri Brahim, Djerioui Khayra
Pages : 16-21
View : 7 | Download : 5
Publication Date : 2019-06-15
Article Type : Other
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