Numerical identification of multiparameters in the space fractional advection dispersion equation by final observations. (English) Zbl 1264.65118
Summary: This paper deals with an inverse problem for identifying multiparameters in 1D space fractional advection dispersion equation (FADE) on a finite domain with final observations. The parameters to be identified are the fractional order, the diffusion coefficient, and the average velocity in the FADE. The forward problem is solved by a finite difference scheme, and then an optimal perturbation regularization algorithm is introduced to determine the three parameters simultaneously. Numerical inversions are performed both with the accurate data and noisy data, and several factors having influences on realization of the algorithm are discussed. The inversion solutions are in good approximations to the exact solutions demonstrating the efficiency of the proposed algorithm.
MSC:
| 65L12 | Finite difference and finite volume methods for ordinary differential equations |
| 65L09 | Numerical solution of inverse problems involving ordinary differential equations |
| 35R11 | Fractional partial differential equations |
| 35R30 | Inverse problems for PDEs |
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