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# Homotopy Method for Parameter Determination of Solute Transport with Fractional Advection-dispersion Equation

Hui Wei1,2,3, Wen Chen1,2,4, HongGuang Sun1,2
Institute of Soft Matter Mechanics, College of Mechanics and Materials, Hohai University, Nanjing, China, 210098.
State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, China, 210098.
Department of Mathematics, College of Science, Anhui University of Science and Technology, Anhui, China, 232001.
Corresponding author. Email: chenwen@hhu.edu.cn

Computer Modeling in Engineering & Sciences 2014, 100(2), 85-103. https://doi.org/10.3970/cmes.2014.100.085

### Abstract

The unknown parameters are critical factors in fractional derivative advection-dispersion equation describing the solute transport in soil. For examples, the fractional derivative order is the index of anomalous dispersion, diffusion coefficient represents the dispersion ability of media and average pore-water velocity denotes the main trend of transport, etc. This paper is to develop a homotopy method to determine the unknown parameters of solute transport with spatial fractional derivative advection-dispersion equation in soil. The homotopy method can be easily developed to solve parameter determination problems of fractional derivative equations whose analytical solutions are difficult to obtain. The sigmoid function is involved to adjust the homotopy parameter during the iterative processes. Numerical results show that the presented method is efficient and feasible in several benchmark examples.

### Keywords

Homotopy method, Parameter determination, Fractional advection-dispersion equation, Sigmoid function.

Wei, H., Chen, W., Sun, H. (2014). Homotopy Method for Parameter Determination of Solute Transport with Fractional Advection-dispersion Equation. CMES-Computer Modeling in Engineering & Sciences, 100(2), 85–103. This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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