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Jacobi Spectral Collocation Method for the Time Variable-Order Fractional Mobile-Immobile Advection-Dispersion Solute Transport Model

Part of: Basic linear algebra Difference equations Partial differential equations, initial value and time-dependent initial-boundary value problems Real functions Difference and functional equations

Published online by Cambridge University Press:  20 July 2016

Heping Ma  and
Yubo Yang
Heping Ma*
Affiliation:
Department of Mathematics, Shanghai University, Shanghai 200444, China
Yubo Yang*
Affiliation:
Department of Mathematics, Shanghai University, Shanghai 200444, China Nanhu College, Jiaxing University, Jiaxing, Zhejiang 314001, China
*
*Corresponding author. Email addresses:hpma@shu.edu.cn (H. Ma), boydman_xm@hotmail.com (Y. Yang)
*Corresponding author. Email addresses:hpma@shu.edu.cn (H. Ma), boydman_xm@hotmail.com (Y. Yang)
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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 derivativeJacobi polynomialsspectral collocation methodMobile-immobile advection-dispersion model

MSC classification

Secondary: 26A33: Fractional derivatives and integrals 65M70: Spectral, collocation and related methods 15A99: Miscellaneous topics 39A70: Difference operators

Information

Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 6 , Issue 3 , August 2016 , pp. 337 - 352
Copyright
Copyright © Global-Science Press 2016 

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