Journal of Applied & Computational Mathematics

Fenga L

Publications

• Research Article
  High-order Accurate Numerical Methods for Solving the Space Fractional Advection-dispersion Equation
  Author(s): Fenga L, Zhuangb P, Liu F and Turnera IFenga L, Zhuangb P, Liu F and Turnera I
  
  In this paper, we consider a type of space fractional advection-dispersion equation, which is obtained from the classical advection-diffusion equation by replacing the spatial derivatives with a generalized derivative of fractional order. Firstly, we utilize the modified weighted and shifted Grunwald difference operators to approximate the Riemann-Liouville fractional derivatives and present the finite volume method. Specifically, we discuss the Crank-Nicolson scheme and solve it in matrix form. Secondly, we prove that the scheme is unconditionally stable and convergent with the accuracy of O(τ2 + h2). Furthermore, we apply an extrapolation method to improve the convergence order, which can be O(τ4 + h4). Finally, two numerical examples are given to show the effectiveness of the numerical method, and the results are in excellent agreement with the theoretical analysis. .. Read More»
  DOI: 10.4172/2168-9679.1000279

  Abstract PDF