The Experts below are selected from a list of 282 Experts worldwide ranked by ideXlab platform

Ian Turner - One of the best experts on this subject based on the ideXlab platform.

  • numerical analysis of a new space time variable fractional order advection Dispersion Equation
    Science & Engineering Faculty, 2014
    Co-Authors: Hongmei Zhang, Pinghui Zhuang, Ian Turner, Fawang Liu, Vo Anh
    Abstract:

    Many physical processes appear to exhibit fractional order behavior that may vary with time and/or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider a new space–time variable fractional order advection–Dispersion Equation on a finite domain. The Equation is obtained from the standard advection–Dispersion Equation by replacing the first-order time derivative by Coimbra’s variable fractional derivative of order α(x)∈(0,1]α(x)∈(0,1], and the first-order and second-order space derivatives by the Riemann–Liouville derivatives of order γ(x,t)∈(0,1]γ(x,t)∈(0,1] and β(x,t)∈(1,2]β(x,t)∈(1,2], respectively. We propose an implicit Euler approximation for the Equation and investigate the stability and convergence of the approximation. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

  • a second order accurate numerical approximation for the riesz space fractional advection Dispersion Equation
    The Proceedings of the Fifth Symposium on Fractional Differentiation and Its Applications, 2012
    Co-Authors: Shujun Shen, Ian Turner, J. Chen
    Abstract:

    In this paper, we consider a space Riesz fractional advection-Dispersion Equation. The Equation is obtained from the standard advection-diffusion Equation by replacing the ¯rst-order and second-order space derivatives by the Riesz fractional derivatives of order β 1 Є (0; 1) and β2 Є(1; 2], respectively. Riesz fractional advection and Dispersion terms are approximated by using two fractional centered difference schemes, respectively. A new weighted Riesz fractional ¯nite difference approximation scheme is proposed. When the weighting factor Ѳ = 1/2, a second- order accurate numerical approximation scheme for the Riesz fractional advection-Dispersion Equation is obtained. Stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

  • the fundamental solution and numerical solution of the riesz fractional advection Dispersion Equation
    Ima Journal of Applied Mathematics, 2008
    Co-Authors: Shujun Shen, Ian Turner
    Abstract:

    In this paper, we consider a Riesz fractional advection-Dispersion Equation (RFADE), which is derived from the kinetics of chaotic dynamics. The RFADE is obtained from the standard advection-Dispersion Equation by replacing the first-order and second-order space derivatives by the Riesz fractional derivatives of order a e (0, 1) and fi e (1, 2], respectively. We derive the fundamental solution for the Riesz fractional advection-Dispersion Equation with an initial condition (RFADE-IC). We investigate a discrete random walk model based on an explicit finite-difference approximation for the RFADE-IC and prove that the random walk model belongs to the domain of attraction of the corresponding stable distribution. We also present explicit and implicit difference approximations for the Riesz fractional advection-Dispersion Equation with initial and boundary conditions (RFADE-IBC) in a finite domain. Stability and convergence of these numerical methods for the RFADE-IBC are discussed. Some numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.

  • The fundamental solution and numerical solution of the Riesz fractional advection–Dispersion Equation
    IMA Journal of Applied Mathematics, 2008
    Co-Authors: Shujun Shen, Fawang Liu, Vo Anh, Ian Turner
    Abstract:

    In this paper, we consider a Riesz fractional advection-Dispersion Equation (RFADE), which is derived from the kinetics of chaotic dynamics. The RFADE is obtained from the standard advection-Dispersion Equation by replacing the first-order and second-order space derivatives by the Riesz fractional derivatives of order a e (0, 1) and fi e (1, 2], respectively. We derive the fundamental solution for the Riesz fractional advection-Dispersion Equation with an initial condition (RFADE-IC). We investigate a discrete random walk model based on an explicit finite-difference approximation for the RFADE-IC and prove that the random walk model belongs to the domain of attraction of the corresponding stable distribution. We also present explicit and implicit difference approximations for the Riesz fractional advection-Dispersion Equation with initial and boundary conditions (RFADE-IBC) in a finite domain. Stability and convergence of these numerical methods for the RFADE-IBC are discussed. Some numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.

  • the fundamental and numerical solutions of the riesz space fractional reaction Dispersion Equation
    Anziam Journal, 2008
    Co-Authors: J. Chen, Ian Turner
    Abstract:

    A Riesz space-fractional reaction–Dispersion Equation (RSFRDE) is obtained from the classical reaction–Dispersion Equation (RDE) by replacing the second-order space derivative with a Riesz derivative of order beta in (1,2]. In this paper, using Laplace and Fourier transforms, we obtain the fundamental solution for a RSFRDE. We propose an explicit finite-difference approximation for a RSFRDE in a bounded spatial domain, and analyse its stability and convergence. Some numerical examples are presented. doi:10.1017/S1446181108000333

Pinghui Zhuang - One of the best experts on this subject based on the ideXlab platform.

  • numerical analysis of a new space time variable fractional order advection Dispersion Equation
    Science & Engineering Faculty, 2014
    Co-Authors: Hongmei Zhang, Pinghui Zhuang, Ian Turner, Fawang Liu, Vo Anh
    Abstract:

    Many physical processes appear to exhibit fractional order behavior that may vary with time and/or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider a new space–time variable fractional order advection–Dispersion Equation on a finite domain. The Equation is obtained from the standard advection–Dispersion Equation by replacing the first-order time derivative by Coimbra’s variable fractional derivative of order α(x)∈(0,1]α(x)∈(0,1], and the first-order and second-order space derivatives by the Riemann–Liouville derivatives of order γ(x,t)∈(0,1]γ(x,t)∈(0,1] and β(x,t)∈(1,2]β(x,t)∈(1,2], respectively. We propose an implicit Euler approximation for the Equation and investigate the stability and convergence of the approximation. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

  • time fractional advection Dispersion Equation
    Journal of Applied Mathematics and Computing, 2003
    Co-Authors: Ian Turner, Pinghui Zhuang
    Abstract:

    A time fractional advection-Dispersion Equation is obtained from the standard advection-Dispersion Equation by replacing the firstorder derivative in time by a fractional derivative in time of order α(0<α<-1). Using variable transformation, Mellin and Laplace transforms, and properties of H-functions, we derive the complete solution of this time fractional advection-Dispersion Equation.

  • Time fractional advection-Dispersion Equation
    Journal of Applied Mathematics and Computing, 2003
    Co-Authors: Ian Turner, Pinghui Zhuang
    Abstract:

    A time fractional advection-Dispersion Equation is obtained from the standard advection-Dispersion Equation by replacing the firstorder derivative in time by a fractional derivative in time of order α(0

Fenghui Huang - One of the best experts on this subject based on the ideXlab platform.

  • the fundamental solution of the space time fractional advection Dispersion Equation
    Journal of Applied Mathematics and Computing, 2005
    Co-Authors: Fenghui Huang
    Abstract:

    A space-time fractional advection-Dispersion Equation (ADE) is a generalization of the classical ADE in which the first-order time derivative is replaced with Caputo derivative of order α ∈ (0, 1], and the second-order space derivative is replaced with a Riesz-Feller derivative of order β ∈ (0, 2]. We derive the solution of its Cauchy problem in terms of the Green functions and the representations of the Green function by applying its Fourier-Laplace transforms. The Green function also can be interpreted as a spatial probability density function (pdf) evolving in time. We do the same on another kind of space-time fractional advection-Dispersion Equation whose space and time derivatives both replacing with Caputo derivatives.

Yingzhen Lin - One of the best experts on this subject based on the ideXlab platform.

  • approximate solution of the fractional advection Dispersion Equation
    Computer Physics Communications, 2010
    Co-Authors: Wei Jiang, Yingzhen Lin
    Abstract:

    Abstract In this paper, we consider practical numerical method to solve a space–time fractional advection–Dispersion Equation with variable coefficients on a finite domain. The Equation is obtained from the standard advection–Dispersion Equation by replacing the first-order time derivative by the Caputo fractional derivative, and the first-order and second-order space derivatives by the Riemann–Liouville fractional derivative, respectively. Here, a new method for solving this Equation is proposed in the reproducing kernel space. The representation of solution is given by the form of series and the n -term approximation solution is obtained by truncating the series. The method is easy to implement and the numerical results show the accuracy of the method.

  • Approximate solution of the fractional advection―Dispersion Equation
    Computer Physics Communications, 2010
    Co-Authors: Wei Jiang, Yingzhen Lin
    Abstract:

    Abstract In this paper, we consider practical numerical method to solve a space–time fractional advection–Dispersion Equation with variable coefficients on a finite domain. The Equation is obtained from the standard advection–Dispersion Equation by replacing the first-order time derivative by the Caputo fractional derivative, and the first-order and second-order space derivatives by the Riemann–Liouville fractional derivative, respectively. Here, a new method for solving this Equation is proposed in the reproducing kernel space. The representation of solution is given by the form of series and the n -term approximation solution is obtained by truncating the series. The method is easy to implement and the numerical results show the accuracy of the method.

Wei Jiang - One of the best experts on this subject based on the ideXlab platform.

  • approximate solution of the fractional advection Dispersion Equation
    Computer Physics Communications, 2010
    Co-Authors: Wei Jiang, Yingzhen Lin
    Abstract:

    Abstract In this paper, we consider practical numerical method to solve a space–time fractional advection–Dispersion Equation with variable coefficients on a finite domain. The Equation is obtained from the standard advection–Dispersion Equation by replacing the first-order time derivative by the Caputo fractional derivative, and the first-order and second-order space derivatives by the Riemann–Liouville fractional derivative, respectively. Here, a new method for solving this Equation is proposed in the reproducing kernel space. The representation of solution is given by the form of series and the n -term approximation solution is obtained by truncating the series. The method is easy to implement and the numerical results show the accuracy of the method.

  • Approximate solution of the fractional advection―Dispersion Equation
    Computer Physics Communications, 2010
    Co-Authors: Wei Jiang, Yingzhen Lin
    Abstract:

    Abstract In this paper, we consider practical numerical method to solve a space–time fractional advection–Dispersion Equation with variable coefficients on a finite domain. The Equation is obtained from the standard advection–Dispersion Equation by replacing the first-order time derivative by the Caputo fractional derivative, and the first-order and second-order space derivatives by the Riemann–Liouville fractional derivative, respectively. Here, a new method for solving this Equation is proposed in the reproducing kernel space. The representation of solution is given by the form of series and the n -term approximation solution is obtained by truncating the series. The method is easy to implement and the numerical results show the accuracy of the method.