81 citations · 105 across the 11 of their papers we have counts for
11 papers
Energy stability and convergence of variable-step L1 scheme for the time fractional Swift-Hohenberg model
Xuan Zhao, Ran Yang, Ren-jun Qi +1
A fully implicit numerical scheme is established for solving the time fractional Swift-Hohenberg (TFSH) equation with a Caputo time derivative of order . The variable-st…
Energy stable and norm convergent BDF3 scheme for the Swift-Hohenberg equation
Xuan Zhao, Ran Yang, Zhongqin Xue +1
A fully discrete implicit scheme is proposed for the Swift-Hohenberg model, combining the third-order backward differentiation formula (BDF3) for the time discretization and the se…
Error estimate of the nonuniform type formula for the time fractional diffusion-wave equation
Hong Sun, Yanping Chen, Xuan Zhao
In this paper, a temporal nonuniform type difference scheme is built up for the time fractional diffusion-wave equation with the help of the order reduction technique. The unc…
On some analytic properties of nabla tempered fractional calculus
Yiheng Wei, Linlin Zhao, Xuan Zhao +1
Despite many applications regarding fractional calculus have been reported in literature, it is still unknown how to model some practical process. One major challenge in solving su…
Error analysis of the implicit variable-step BDF2 method for the molecular beam epitaxial model with slope selection
Xuan Zhao, Haifeng Zhang, Hong Sun
We derive unconditionally stable and convergent variable-step BDF2 scheme for solving the MBE model with slope selection. The discrete orthogonal convolution kernels of the variabl…
Convergence analysis of variable steps BDF2 method for the space fractional Cahn-Hilliard model
Xuan Zhao, Zhongqin Xue
An implicit variable-step BDF2 scheme is established for solving the space fractional Cahn-Hilliard equation, involving the fractional Laplacian, derived from a gradient flow in th…
Asymptotically compatible energy of variable-step fractional BDF2 formula for time-fractional Cahn-Hilliard model
Hong-lin Liao, Nan Liu, Xuan Zhao
A new discrete energy dissipation law of the variable-step fractional BDF2 (second-order backward differentiation formula) scheme is established for time-fractional Cahn-Hilliard m…
High Order Compact Finite Difference Methods for Non-Fickian Flows in Porous Media
Xuan Zhao, Ziyan Li, Xiaoli Li
In this work, fourth-order compact block-centered finite difference (CBCFD) schemes combined with the Crank-Nicolson discretization are constructed and analyzed for solving parabol…
Superconvergence Points For The Spectral Interpolation Of Riesz Fractional Derivatives
Beichuan Deng, Zhimin Zhang, Xuan Zhao
In this paper, superconvergence points are located for the approximation of the Riesz derivative of order using classical Lobatto-type polynomials when and general…
Adaptive Finite Element Method for fractional differential equations using Hierarchical Matrices
Xuan Zhao, Xiaozhe Hu, Wei Cai +1
A robust and fast solver for the fractional differential equation (FDEs) involving the Riesz fractional derivative is developed using an adaptive finite element method on non-unifo…
Superconvergence points of fractional spectral interpolation
Xuan Zhao, Zhimin Zhang
We investigate superconvergence properties of the spectral interpolation involving fractional derivatives. Our interest in this superconvergence problem is, in fact, twofold: when…