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Yıl 2019, Cilt 1, Sayı 1, 16 - 21, 15.06.2019

Öz

Kaynakça

  • [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.

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

Yıl 2019, Cilt 1, Sayı 1, 16 - 21, 15.06.2019

Öz

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.

Kaynakça

  • [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.

Ayrıntılar

Birincil Dil İngilizce
Konular Bilgisayar Bilimleri, Disiplinler Arası Uygulamalar
Bölüm Articles
Yazarlar

Nouiri BRAHİM (Sorumlu Yazar)
Laboratory of Pure and Applied Mathematics, Mohamed Boudiaf University, M'sila
0000-0001-5365-6116
Algeria


Djerioui KHAYRA Bu kişi benim
Mohamed Boudiaf University, M'sila
Algeria

Yayımlanma Tarihi 15 Haziran 2019
Yayınlandığı Sayı Yıl 2019, Cilt 1, Sayı 1

Kaynak Göster

Bibtex @konferans bildirisi { pims609634, journal = {Proceedings of International Mathematical Sciences}, issn = {2717-6355}, address = {Maltepe University, Istanbul}, publisher = {İbrahim ÇANAK}, year = {2019}, volume = {1}, pages = {16 - 21}, doi = {}, title = {An Inverse Diffusion-Wave Problem Defined in Heterogeneous Medium with Additional Boundary Measurement}, key = {cite}, author = {Brahim, Nouiri and Khayra, Djerioui} }
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