scholarly journals SHARED VALUES AND BOREL EXCEPTIONAL VALUES FOR HIGH ORDER DIFFERENCE OPERATORS

2016 ◽  
Vol 53 (1) ◽  
pp. 49-60
Author(s):  
Liangwen Liao ◽  
Jie Zhang
Keyword(s):  
Shared Values ◽  
High Order ◽  
Difference Operators ◽  
Order Difference ◽  
Borel Exceptional Values

A High-Order Difference Scheme for the Space and Time Fractional Bloch–Torrey Equation

2018 ◽  
Vol 18 (1) ◽  
pp. 147-164 ◽  
Author(s):  
Yun Zhu ◽  
Zhi-Zhong Sun
Keyword(s):  
Fractional Derivative ◽  
Difference Scheme ◽  
Dimensional Space ◽  
High Order ◽  
Stability And Convergence ◽  
Difference Operators ◽  
Riesz Fractional Derivative ◽  
Central Difference ◽  
Order Difference ◽  
Space And Time

AbstractIn this paper, a high-order difference scheme is proposed for an one-dimensional space and time fractional Bloch–Torrey equation. A third-order accurate formula, based on the weighted and shifted Grünwald–Letnikov difference operators, is used to approximate the Caputo fractional derivative in temporal direction. For the discretization of the spatial Riesz fractional derivative, we approximate the weighed values of the Riesz fractional derivative at three points by the fractional central difference operator. The unique solvability, unconditional stability and convergence of the scheme are rigorously proved by the discrete energy method. The convergence order is 3 in time and 4 in space in {L_{1}(L_{2})}-norm. Two numerical examples are implemented to testify the accuracy of the numerical solution and the efficiency of the difference scheme.

scholarly journals ENTIRE FUNCTIONS SHARING ZERO CM WITH THEIR HIGH ORDER DIFFERENCE OPERATORS

2014 ◽  
Vol 18 (3) ◽  
pp. 701-709 ◽  
Author(s):  
Jie Zhang ◽  
Jianjun Zhang ◽  
Liangwen Liao
Keyword(s):  
Entire Functions ◽  
High Order ◽  
Difference Operators ◽  
Order Difference

scholarly journals An infinite family of higher-order difference operators that commute with Ruijsenaars operators of type A

2021 ◽  
Vol 111 (4) ◽  
Author(s):  
Masatoshi Noumi ◽  
Ayako Sano
Keyword(s):  
Infinite Family ◽  
Type A ◽  
Higher Order ◽  
Difference Operators ◽  
Order Difference

AbstractWe introduce a new infinite family of higher-order difference operators that commute with the elliptic Ruijsenaars difference operators of type A. These operators are related to Ruijsenaars’ operators through a formula of Wronski type.

scholarly journals A pseudopotential multiphase lattice Boltzmann model based on high-order difference

2018 ◽  
Vol 127 ◽  
pp. 234-243 ◽  
Author(s):  
Zhangrong Qin ◽  
Wanling Zhao ◽  
Yanyan Chen ◽  
Chaoying Zhang ◽  
Binghai Wen
Keyword(s):  
Lattice Boltzmann ◽  
High Order ◽  
Lattice Boltzmann Model ◽  
Order Difference ◽  
Model Based ◽  
Boltzmann Model
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