An Inverse Diffusion-Wave Problem Defined in Heterogeneous Medium with Additional Boundary Measurement
An Inverse Diffusion-Wave Problem Defined in Heterogeneous Medium with Additional Boundary Measurement
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.
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- [1] D. Zhang, G. Li, X. Jia and H. Li, Simultaneous Inversion for Space-Dependent Difiusion
Coeficient and Source Magnitude in the Time Fractional Difiusion Equation. J. Math.
Research. Vol. 5, No. 2; 2013.
- [2] J.Huang, Y.Tang, L.Vazquez, J.Yang, Two nite difierence schemes for time-fractional
difiusion-wave equation. Numer. Algor. 64, 707-720 (2013).
- [3] C. Li, F. Zeng, Numerical Methods for Fractional Calculus, CRC Press Taylor&Francis
Group, 2015.
- [4] Z. Amina, Etude d'un probleme inverse pour une equation de difiusion fractionnaire, Master
thesis, Mohamed Boudiaf University, M'sila, Algeria, 2018.
- [5] A. Nour Elhouda, Probleme inverse pour une equation de difiusion-onde fractionnaire,
Master thesis, Mohamed Boudiaf University, M'sila, Algeria, 2019.