A class of second order difference approximations for solving space fractional diffusion equations
A class of second order approximations, called the weighted and shifted Grünwald
difference (WSGD) operators, are proposed for Riemann-Liouville fractional derivatives, with …
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
In this paper, compact finite difference schemes for the modified anomalous fractional sub-
diffusion equation and fractional diffusion-wave equation are studied. Schemes proposed …
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 …
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 …
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
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 …
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
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 …
derivative are developed. Then a second‐order numerical scheme for a Riemann–Liouvile …
Circulant and skew-circulant splitting iteration for fractional advection–diffusion equations
An implicit second-order finite difference scheme, which is unconditionally stable, is
employed to discretize fractional advection–diffusion equations with constant coefficients …
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 …
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
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 …
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
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 …
subject to Neumann boundary conditions. The proposed scheme is second-order accurate …