二维带弱奇异核抛物型积分微分方程的交替方向隐式有限差分格式  

ALTERNATING DIRECTION IMPLICIT FINITE DIFFERENCE METHOD FOR TWO-DIMENSIONAL PARABOLIC-TYPE INTEGRO-DIFFERENTIAL EQUATIONS WITH A WEAKLY SINGULAR KERNEL

作　　者：杨雪花 蒋小玄 刘艳玲 张海湘 Yang Xuehua;Jiang Xiaoxuan;Liu Yanling;Zhang Haixiang(College of Sciences,Hunan University of Technology,Zhuzhou 412007)

机构地区：[1]湖南工业大学理学院,株洲412007

出　　处：《高等学校计算数学学报》2022年第3期267-284,共18页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(12126321);湖南省自然科学基金(2022JJ50083,2021JJ30209);湖南省教育厅科研项目(21B0550)。

摘　　要：In this paper,an alternating direction implicit(ADI)finite difference method is considered to study the numerical solution of two-dimensional fractional evolutionary equations(parabolic integro-difffferential equations with a weakly singular kernel).The backward-Euler technique is used in the time direction,and the first-order convolution formula is used to approximate the integral term,and then the finite difference method is used in the space direction to obtain the ADI fully discrete difference scheme.We use the discrete energy method to prove that the fully discrete scheme is unconditionally stable with convergence order O(k+h_(x)^(2)+h_(y)^(2)),where k denotes the time step and hx and hy denote the space step in the x and y directions,respectively.Finally,some numerical examples are given to demonstrate the validity of the theoretical analysis.

关 键 词：Fractional evolutionary equation alternate direction implicit difference method first-order convolution quadrature stability and convergence discrete energy method 

分 类 号：O241.82[理学—计算数学]