659 citations · 1k across the 9 of their papers we have counts for
9 papers
A Spectral Localization Method for Time-Fractional Integro-Differential Equations with Nonsmooth Data
Lijing Zhao, Rui Zhao, Wenyi Tian +1
In this work, we develop a localized numerical scheme with low regularity requirements for solving time-fractional integro-differential equations. First, a fully discrete numerical…
Analysis of a WSGD scheme for backward fractional Feynman-Kac equation with nonsmooth data
Liyao Hao, Wenyi Tian
In this paper, we propose and analyze a second-order time-stepping numerical scheme for the inhomogeneous backward fractional Feynman-Kac equation with nonsmooth initial data. The…
Crank-Nicolson schemes for sub-diffusion equations with nonsingular and singular source terms in time
Han Zhou, Wenyi Tian
In this work, two Crank-Nicolson schemes without corrections are developed for sub-diffusion equations. First, we propose a Crank-Nicolson scheme without correction for problems wi…
Two time-stepping schemes for sub-diffusion equations with singular source terms
Han Zhou, Wenyi Tian
Singular source terms in sub-diffusion equations may lead to the unboundedness of solutions, which will bring a severe reduction of convergence order of existing time-stepping sche…
An ADMM-Newton-CNN Numerical Approach to a TV Model for Identifying Discontinuous Diffusion Coefficients in Elliptic Equations: Convex Case with Gradient Observations
Wenyi Tian, Xiaoming Yuan, Hangrui Yue
Identifying the discontinuous diffusion coefficient in an elliptic equation with observation data of the gradient of the solution is an important nonlinear and ill-posed inverse pr…
Boundary problems for the fractional and tempered fractional operators
Weihua Deng, Buyang Li, Wenyi Tian +1
For characterizing the Brownian motion in a bounded domain: , it is well-known that the boundary conditions of the classical diffusion equation just rely on the given informatio…
Polynomial Spectral collocation Method for Space Fractional Advection-Diffusion Equation
WenYi Tian, Weihua Deng, Yujiang Wu
This paper discusses the spectral collocation method for numerically solving nonlocal problems: one dimensional space fractional advection-diffusion equation; and two dimensional l…
Compact Finite Difference Approximations for Space Fractional Diffusion Equations
Han Zhou, WenYi Tian, Weihua Deng
Based on the weighted and shifted Grünwald difference (WSGD) operators [24], we further construct the compact finite difference discretizations for the fractional operators. Then t…
A Class of Second Order Difference Approximation for Solving Space Fractional Diffusion Equations
WenYi Tian, Han Zhou, Weihua Deng
A class of second order approximations, called the weighted and shifted Grünwald difference operators, are proposed for Riemann-Liouville fractional derivatives, with their effecti…