A class of second order difference approximations for solving space fractional diffusion equations

WY Tian, H Zhou, W Deng - Mathematics of Computation, 2015 - ams.org
A class of second order approximations, called the weighted and shifted Grünwald
difference (WSGD) operators, are proposed for Riemann-Liouville fractional derivatives, with …

Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation

Z Wang, S Vong - Journal of Computational Physics, 2014 - Elsevier
In this paper, compact finite difference schemes for the modified anomalous fractional sub-
diffusion equation and fractional diffusion-wave equation are studied. Schemes proposed …

High order schemes for the tempered fractional diffusion equations

C Li, W Deng - Advances in computational mathematics, 2016 - Springer
Lévy flight models whose jumps have infinite moments are mathematically used to describe
the superdiffusion in complex systems. Exponentially tempering Lévy measure of Lévy …

New approximations for solving the Caputo-type fractional partial differential equations

J Ren, Z Sun, W Dai - Applied Mathematical Modelling, 2016 - Elsevier
Partial differential equations with the Caputo-type fractional derivative have been used in
many engineering applications. Because the Caputo-type fractional derivative is an integral …

A high‐order compact scheme for the nonlinear fractional K lein–G ordon equation

S Vong, Z Wang - Numerical Methods for Partial Differential …, 2015 - Wiley Online Library
In this article, a high‐order finite difference scheme for a kind of nonlinear fractional Klein–
Gordon equation is derived. The time fractional derivative is described in the Caputo sense …

High‐order compact difference schemes for the modified anomalous subdiffusion equation

H Ding, C Li - Numerical Methods for Partial Differential …, 2016 - Wiley Online Library
In this article, two kinds of high‐order compact finite difference schemes for second‐order
derivative are developed. Then a second‐order numerical scheme for a Riemann–Liouvile …

Circulant and skew-circulant splitting iteration for fractional advection–diffusion equations

W Qu, SL Lei, SW Vong - International Journal of Computer …, 2014 - Taylor & Francis
An implicit second-order finite difference scheme, which is unconditionally stable, is
employed to discretize fractional advection–diffusion equations with constant coefficients …

A new family of difference schemes for space fractional advection diffusion equation

C Li, W Deng - Advances in Applied Mathematics and Mechanics, 2017 - cambridge.org
The second order weighted and shifted Grünwald difference (WSGD) operators are
developed in [Tian, Zhou and Deng, Math. Comput., 84 (2015), pp. 1703–1727] to solve …

Finite difference schemes for two-dimensional time-space fractional differential equations

Z Wang, S Vong, SL Lei - International Journal of Computer …, 2016 - Taylor & Francis
In this paper, finite difference schemes for differential equations with both temporal and
spatial fractional derivatives are studied. When the order of the time fractional derivative is in …

High order difference schemes for a time fractional differential equation with Neumann boundary conditions

S Vong, Z Wang - East Asian Journal on Applied Mathematics, 2014 - cambridge.org
A compact finite difference scheme is derived for a time fractional differential equation
subject to Neumann boundary conditions. The proposed scheme is second-order accurate …