Journal ArticleDOI
Finite difference approximations for two-sided space-fractional partial differential equations
TLDR
In this paper, the authors examined some practical numerical methods to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain, and the stability, consistency, and (therefore) convergence of the methods are discussed.About:
This article is published in Applied Numerical Mathematics.The article was published on 2006-01-01. It has received 836 citations till now. The article focuses on the topics: Numerical partial differential equations & First-order partial differential equation.read more
Citations
More filters
Journal ArticleDOI
A second-order accurate numerical approximation for the fractional diffusion equation
TL;DR: It is shown that the fractional Crank-Nicholson method based on the shifted Grunwald formula is unconditionally stable and compared with the exact analytical solution for its order of convergence.
Journal ArticleDOI
A class of second order difference approximations for solving space fractional diffusion equations
TL;DR: A class of second order approximations, called the weighted and shifted Grunwald difference (WSGD) operators, are proposed for Riemann-Liouville fractional derivatives, with their effective applications to numerically solving space fractional diffusion equations in one and two dimensions.
Journal ArticleDOI
Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
TL;DR: In this article, the Riesz fractional diffusion equation (RFDE) and RFADE (RFADE) were considered and analytic solutions of both the RFDE and the RFADE were derived.
Journal ArticleDOI
Finite difference methods for two-dimensional fractional dispersion equation
TL;DR: In this article, a practical alternating directions implicit method to solve a class of two-dimensional initial-boundary value fractional partial differential equations with variable coefficients on a finite domain is discussed.
Journal ArticleDOI
Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
Cem Çelik,Melda Duman +1 more
TL;DR: The Crank-Nicolson method is applied to a fractional diffusion equation which has the Riesz fractional derivative, and it is obtained that the method is unconditionally stable and convergent.
References
More filters
Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
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
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.
Journal ArticleDOI
Difference Methods for Initial-Value Problems.
Book
Analysis of Numerical Methods
TL;DR: Reference Record created on 2005-11-18, modified on 2016-08-08 as discussed by the authors, created on 2011-11 -18, created on 2006-11 18 and modified on 2008-08 -08,08
Related Papers (5)
Finite difference approximations for fractional advection-dispersion flow equations
The random walk's guide to anomalous diffusion: a fractional dynamics approach
Ralf Metzler,Joseph Klafter +1 more