一类Riesz空间分数阶对流弥散方程的差分方法  

Difference methods for a class of Riesz space fractional convection dispersion equations

作　　者：张治国 陈豫眉 梁倩 ZHANG Zhiguo;CHEN Yumei;LIANG Qian(College of Mathematics and Information,China West Normal University,Nanchong,Sichuan 637009,China;College of Commonly-required Mathematics,China West Normal University,Nanchong,Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009 [2]西华师范大学公共数学学院,四川南充637009

出　　处：《内江师范学院学报》2022年第12期39-44,共6页Journal of Neijiang Normal University

基　　金：国家自然科学基金面上项目(11971097)。

摘　　要：对带有分数阶边界条件的一类Riesz空间分数阶方程,提出了求解该方程的隐式差分格式,得到了离散后的矩阵格式.理论分析了隐式差分格式解满足存在唯一性、具有无条件稳定以及依无穷范数收敛的特性.所给数值算例验证了隐式差分方法的可行性.For a class of Riesz space fractional order equation with fractional boundary condition, an implicit difference scheme of the equation is proposed, and the discrete matrix scheme is worked out. Moreover, theoretical analysis is conducted to prove the solution to the implicit difference scheme is unique in terms of existence, unconditional in terms of stability and with convergence of solutions in infinite norm. The obtained results of numerical examples proved the feasibility of the implicit difference scheme.

关 键 词：Riesz空间分数阶 隐式差分格式 存在性 稳定性 收敛性 

分 类 号：O241.82[理学—计算数学]