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A characteristic difference method for the variable-order fractional advection-diffusion equation

  • S. Shen
  • F. Liu
  • V. Anh
  • I. Turner
  • J. Chen
Computational mathematics

Abstract

In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term (VOFADE-NST) on a finite domain. Combining the characteristic method and the finite difference method, a characteristic finite difference method for solving the VOFADE-NST is presented. Its stability and convergence are analyzed. This new method is shown to be more efficient and superior to the standard finite difference method. Numerical experiments are carried out and the results demonstrate the effectiveness of theoretical analysis.

Keywords

Fractional advection-diffusion equation Characteristic finite difference method Stability and convergence Variable-order fractional order derivative 

Mathematics Subject Classification

26A33 65M12 65M06 

Notes

Acknowledgements

The work was supported by the National Natural Science Foundation of China grant 11001090 and 11101344, the Natural Science Foundation of Huaqiao University grant 08BS507, the Australian Research Council grant DP120103770, and the Natural Science Foundation of Fujian province grant 2010J05009.

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Copyright information

© Korean Society for Computational and Applied Mathematics 2013

Authors and Affiliations

  1. 1.School of Mathematical SciencesHuaqiao UniversityQuanzhouChina
  2. 2.School of Mathematical SciencesQueensland University of TechnologyBrisbaneAustralia
  3. 3.School of SciencesJimei UniversityXiamenChina

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