Finite difference approximations for fractional advection-dispersion flow equations
TL;DR: In this paper, the authors developed practical numerical methods to solve one dimensional fractional advection-dispersion equations with variable coefficients on a finite domain and demonstrated the practical application of these results is illustrated by modeling a radial flow problem.
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About: This article is published in Journal of Computational and Applied Mathematics. The article was published on 01 Nov 2004. and is currently open access. The article focuses on the topics: Fractional calculus & Finite difference.
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Citations
An Improved Algorithm Based on Finite Difference Schemes for Fractional Boundary Value Problems with Nonsmooth Solution
Zhaopeng Hao,Wanrong Cao +1 more
TL;DR: It is demonstrated that, with the use of the proposed algorithm, the improved WSGD and FCD schemes can achieve higher accuracy than the original ones for nonsmooth solution.
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A fourth-order dissipation-preserving algorithm with fast implementation for space fractional nonlinear damped wave equations
TL;DR: A novel high-accuracy dissipation-preserving finite difference scheme is constructed by using the new fourth-order fractional central difference operator using the toeplitz-like differentiation matrix and the computation efficiency is raised by fast Fourier transform.
33
A new Crank–Nicolson finite element method for the time-fractional subdiffusion equation☆
Fanhai Zeng,Changpin Li +1 more
TL;DR: In this paper, a new Crank-Nicolson finite element method for the time-fractional subdiffusion equation is developed, in which a novel time discretization called the modified L1 method is used to discretize the Riemann-Liouville fractional derivative.
33
A Second Order Finite Difference Approximation for the Fractional Diffusion Equation
TL;DR: In this paper, it was shown that the finite difference approximation obtained from the Grünwald-Letnikov formulation, often claimed to be of first order accuracy, is in fact a second order approximation of the fractional derivative at a point away from the grid points.
Finite element method for two‐dimensional time‐fractional tricomi‐type equations
Abstract: In this article, we consider the finite element method (FEM) for two‐dimensional linear time‐fractional Tricomi‐type equations, which is obtained from the standard two‐dimensional linear Tricomi‐type equation by replacing the first‐order time derivative with a fractional derivative (of order α, with 1
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References
•Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
- 19 May 1993
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
•Book
Fractional Integrals and Derivatives: Theory and Applications
Stefan Samko,Anatoly A. Kilbas,O. I. Marichev +2 more
- 08 Dec 1993
TL;DR: Fractional integrals and derivatives on an interval fractional integral integrals on the real axis and half-axis further properties of fractional integral and derivatives, and derivatives of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations with special function kernels applications to differential equations as discussed by the authors.
Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
TL;DR: In this article, the authors consider the specific effects of a bias on anomalous diffusion, and discuss the generalizations of Einstein's relation in the presence of disorder, and illustrate the theoretical models by describing many physical situations where anomalous (non-Brownian) diffusion laws have been observed or could be observed.
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