659 citations · 831 across the 5 of their papers we have counts for
5 papers
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…
Stability and convergence analysis of a class of continuous piecewise polynomial approximations for time fractional differential equations
Han Zhou, Paul Andries Zegeling
We propose and study a class of numerical schemes to approximate time fractional differential equations. The methods are based on the approximation of the Caputo fractional derivat…
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…