659 citations · 2.4k across the 64 of their papers we have counts for
6 papers · 2 filters
High Order Finite Difference Methods on Non-uniform Meshes for Space Fractional Operators
Lijing Zhao, Weihua Deng
In the past decades, the finite difference methods for space fractional operators develop rapidly; to the best of our knowledge, all the existing finite difference schemes, includi…
Nodal discontinuous Galerkin methods for fractional diffusion equations on 2D domain with triangular meshes
Liangliang Qiu, Weihua Deng, Jan Hesthaven
This paper, as the sequel to previous work, develops numerical schemes for fractional diffusion equations on a two-dimensional finite domain with triangular meshes. We adopt the no…
Fourth order quasi-compact difference schemes for (tempered) space fractional diffusion equations
Yanyan Yu, Weihua Deng, Yujiang Wu
The continuous time random walk (CTRW) underlies many fundamental processes in non-equilibrium statistical physics. When the jump length of CTRW obeys a power-law distribution, its…
High order algorithms for the fractional substantial diffusion equation with truncated Lévy flights
Minghua Chen, Weihua Deng
The equation with the time fractional substantial derivative and space fractional derivative describes the distribution of the functionals of the Lévy flights; and the equation is…
Wavelet Galerkin method for fractional elliptic differential equations
Weihua Deng, Yuwei Lin, Zhijiang Zhang
Under the guidance of the general theory developed for classical partial differential equations (PDEs), we investigate the Riesz bases of wavelets in the spaces where fractional PD…
Local discontinuous Galerkin methods for fractional ordinary differential equations
Weihua Deng, Jan S. Hesthaven
This paper discusses the upwinded local discontinuous Galerkin methods for the one-term/multi-term fractional ordinary differential equations (FODEs). The natural upwind choice of…