Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 37, Issue 6, Pages A2813-A2839Publisher
SIAM PUBLICATIONS
DOI: 10.1137/15M1008993
Keywords
fractional advection-dispersion equation; parameter identification; fractional order estimation; modulating functions method
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Funding
- King Abdullah University of Science and Technology (KAUST)
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In this paper, a new method, based on the so-called modulating functions, is proposed to estimate average velocity, dispersion coefficient, and differentiation order in a space-fractional advection-dispersion equation, where the average velocity and the dispersion coefficient are space-varying. First, the average velocity and the dispersion coefficient are estimated by applying the modulating functions method, where the problem is transformed into a linear system of algebraic equations. Then, the modulating functions method combined with a Newton's iteration algorithm is applied to estimate the coefficients and the differentiation order simultaneously. The local convergence of the proposed method is proved. Numerical results are presented with noisy measurements to show the effectiveness and robustness of the proposed method. It is worth mentioning that this method can be extended to general fractional partial differential equations.
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