ZHU Xiaogang, NIE Yufeng. An Operational Matrix Method for Fractional Advection-Diffusion Equations With Variable Coefficients[J]. Applied Mathematics and Mechanics, 2018, 39(1): 104-112. doi: 10.21656/1000-0887.380041
Citation: ZHU Xiaogang, NIE Yufeng. An Operational Matrix Method for Fractional Advection-Diffusion Equations With Variable Coefficients[J]. Applied Mathematics and Mechanics, 2018, 39(1): 104-112. doi: 10.21656/1000-0887.380041

An Operational Matrix Method for Fractional Advection-Diffusion Equations With Variable Coefficients

doi: 10.21656/1000-0887.380041
Funds:  The National Natural Science Foundation of China(11471262; 11501450)
  • Received Date: 2017-02-23
  • Rev Recd Date: 2047-03-19
  • Publish Date: 2018-01-15
  • A numerical method for the Caputo-fractional advection-diffusion equations with variable coefficients was investigated. Based on Chebyshev cardinal functions, an effective operational matrix was derived for Riemann-Liouville fractional integral, and with it, a new operational matrix method was proposed for the fractional advection-diffusion equations with variable coefficients. This method reduces the equation to an algebraic system and is characterized by small computing cost and easy programming. The numerical results and the comparisons with some existing methods illustrate that it is convergent and possesses advantages in accuracy.
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