基于最大模原理的双边空间分数阶方程的二阶隐式有限差分法  

A Kind of Second-order Implicit Finite Difference Methods for Two-sided Space Fractional Partial Differential Equations Based on the Maximum Modulus Principle

作　　者：朱琳[1] 芮洪兴[2] 

机构地区：[1]宁夏大学数学与计算机学院,银川750021 [2]山东大学数学学院,济南250100

出　　处：《重庆师范大学学报（自然科学版）》2015年第3期83-87,共5页Journal of Chongqing Normal University:Natural Science

基　　金：宁夏高等学校科学技术研究项目(No.NGY2013018)

摘　　要：应用最大模原理,给出一类解变系数双边空间分数阶偏微分方程的隐式有限差分格式,并证明这类格式当分数阶导数α∈[17-1/2,2]时无条件稳定且由此得出其收敛阶为O(Δt+h2)。最后给出数值算例验证。Based on the maximum modulus principle, a kind of implicit finite difference schemes for two-sided space fractional partial differential equations with variable coefficient is introduced. This kind of schemes unconditionally stable and convergence rate O（△t＋ h^2） with fractional derivative a belonging to [√17-1/2,2] are proved. Numerical examples are given to show the efficiency and the convergence rate of presented schemes.

关 键 词：变系数双边空间分数阶偏微分方程 有限差分格式 无条件稳定 收敛阶 

分 类 号：O241.82[理学—计算数学]