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A New Family of Difference Schemes for Space Fractional Advection Diffusion Equation

A New Family of Difference Schemes for Space Fractional Advection Diffusion Equation
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Year:    2017

Author:    Can Li, Weihua Deng

Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 2 : pp. 282–306

Abstract

The second order weighted and shifted Grünwald difference (WSGD) operators are developed in [Tian, Zhou and Deng, Math. Comput., 84 (2015), pp. 1703–1727] to solve space fractional partial differential equations. Along this direction, we further design a new family of second order WSGD operators; by properly choosing the weighted parameters, they can be effectively used to discretize space (Riemann-Liouville) fractional derivatives. Based on the new second order WSGD operators, we derive a family of difference schemes for the space fractional advection diffusion equation. By von Neumann stability analysis, it is proved that the obtained schemes are unconditionally stable. Finally, extensive numerical experiments are performed to demonstrate the performance of the schemes and confirm the convergence orders.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.2015.m1069

Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 2 : pp. 282–306

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Riemann-Liouville fractional derivative WSGD operator fractional advection diffusion equation finite difference approximation stability.

Author Details

Can Li

Weihua Deng

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