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Inverting the variable fractional order in a variable-order space-fractional diffusion equation with variable diffusivity: analysis and simulation
- Source :
- Journal of Inverse and Ill-posed Problems. 29:219-231
- Publication Year :
- 2020
- Publisher :
- Walter de Gruyter GmbH, 2020.
-
Abstract
- Variable-order space-fractional diffusion equations provide very competitive modeling capabilities of challenging phenomena, including anomalously superdiffusive transport of solutes in heterogeneous porous media, long-range spatial interactions and other applications, as well as eliminating the nonphysical boundary layers of the solutions to their constant-order analogues. In this paper, we prove the uniqueness of determining the variable fractional order of the homogeneous Dirichlet boundary-value problem of the one-sided linear variable-order space-fractional diffusion equation with some observed values of the unknown solutions near the boundary of the spatial domain. We base on the analysis to develop a spectral-Galerkin Levenberg–Marquardt method and a finite difference Levenberg–Marquardt method to numerically invert the variable order. We carry out numerical experiments to investigate the numerical performance of these methods.
- Subjects :
- Diffusion equation
Applied Mathematics
Mathematical analysis
Finite difference method
Finite difference
Boundary (topology)
010103 numerical & computational mathematics
Inverse problem
01 natural sciences
010101 applied mathematics
Levenberg–Marquardt algorithm
0101 mathematics
Diffusion (business)
Mathematics
Variable (mathematics)
Subjects
Details
- ISSN :
- 15693945 and 09280219
- Volume :
- 29
- Database :
- OpenAIRE
- Journal :
- Journal of Inverse and Ill-posed Problems
- Accession number :
- edsair.doi...........39a38ad803248b9d725c3534efcadd61