Chinese Quarterly Journal of Mathematics ›› 2019, Vol. 34 ›› Issue (3): 259-273.doi: 10.13371/j.cnki.chin.q.j.m.2019.03.004

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Finite Difference Methods for the Time Fractional Advection-diffusion Equation

  

  1. Zhi Xing College of Northwest Normal University Department of Mathematics, University of Bani Walid
  • Received:2018-09-04 Online:2019-09-30 Published:2020-08-23
  • Contact: MA Yan(1985-), female, native of LanZhou, Gansu, a lecturer of Northwest Normal University, M.S.D., engages in numerical methods for partial di®erential equation MUSBAH F S(1980-), female, native of Bani Walid, Libya, a lecturer of University of Bani Walid, ph.D., engages in numerical analysis for fractional calculus, partial differential equation and integral equation.

Abstract: In this paper, three implicit finite difference methods are developed to solve one dimensional time fractional advection-diffusion equation. The fractional derivative is treated by applying right shifted Gr¨unwald-Letnikov formula of order α∈(0, 1). We investigate the stability analysis by using von Neumann method with mathematical induction and prove that these three proposed methods are unconditionally stable. Numerical results are presented to demonstrate the effectiveness of the schemes mentioned in this paper.

Key words: Time fractional advection-di?usion, Finite di?erence method, Gr?unwald-Letnikov formula, Stability, E?ectiveness

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