Volume 6, Issue 3
Jacobi Spectral Collocation Method for the Time Variable-Order Fractional Mobile-Immobile Advection-Dispersion Solute Transport Model

East Asian J. Appl. Math., 6 (2016), pp. 337-352.

Published online: 2018-02

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• Abstract

An efficient high order numerical method is presented to solve the mobile-immobile advection-dispersion model with the Coimbra time variable-order fractional derivative, which is used to simulate solute transport in watershed catchments and rivers. On establishing an efficient recursive algorithm based on the properties of Jacobi polynomials to approximate the Coimbra variable-order fractional derivative operator, we use spectral collocation method with both temporal and spatial discretisation to solve the time variable-order fractional mobile-immobile advection-dispersion model. Numerical examples then illustrate the effectiveness and high order convergence of our approach.

• Keywords

Coimbra variable-order fractional derivative, Jacobi polynomials, spectral collocation method, Mobile-immobile advection-dispersion model.

26A33, 65M70, 15A99, 39A70

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@Article{EAJAM-6-337, author = {}, title = {Jacobi Spectral Collocation Method for the Time Variable-Order Fractional Mobile-Immobile Advection-Dispersion Solute Transport Model}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {6}, number = {3}, pages = {337--352}, abstract = {

An efficient high order numerical method is presented to solve the mobile-immobile advection-dispersion model with the Coimbra time variable-order fractional derivative, which is used to simulate solute transport in watershed catchments and rivers. On establishing an efficient recursive algorithm based on the properties of Jacobi polynomials to approximate the Coimbra variable-order fractional derivative operator, we use spectral collocation method with both temporal and spatial discretisation to solve the time variable-order fractional mobile-immobile advection-dispersion model. Numerical examples then illustrate the effectiveness and high order convergence of our approach.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.141115.060616a}, url = {http://global-sci.org/intro/article_detail/eajam/10802.html} }
TY - JOUR T1 - Jacobi Spectral Collocation Method for the Time Variable-Order Fractional Mobile-Immobile Advection-Dispersion Solute Transport Model JO - East Asian Journal on Applied Mathematics VL - 3 SP - 337 EP - 352 PY - 2018 DA - 2018/02 SN - 6 DO - http://doi.org/10.4208/eajam.141115.060616a UR - https://global-sci.org/intro/article_detail/eajam/10802.html KW - Coimbra variable-order fractional derivative, Jacobi polynomials, spectral collocation method, Mobile-immobile advection-dispersion model. AB -

An efficient high order numerical method is presented to solve the mobile-immobile advection-dispersion model with the Coimbra time variable-order fractional derivative, which is used to simulate solute transport in watershed catchments and rivers. On establishing an efficient recursive algorithm based on the properties of Jacobi polynomials to approximate the Coimbra variable-order fractional derivative operator, we use spectral collocation method with both temporal and spatial discretisation to solve the time variable-order fractional mobile-immobile advection-dispersion model. Numerical examples then illustrate the effectiveness and high order convergence of our approach.

Heping Ma & Yubo Yang. (2020). Jacobi Spectral Collocation Method for the Time Variable-Order Fractional Mobile-Immobile Advection-Dispersion Solute Transport Model. East Asian Journal on Applied Mathematics. 6 (3). 337-352. doi:10.4208/eajam.141115.060616a
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