奇异摄动Volterra积分微分方程的自适应网格方法的一致收敛性分析  

Uniform Convergence Analysis of an Adaptive Grid Method for a Singularly Perturbed Volterra Integro-Differential Equation

作　　者：张永[1] 包小兵[1] 刘利斌 梁颖 ZHANG Yong;BAO Xiao-bing;LIU Li-bin;LIANG Ying(School of Big Data and Artifificial Intelligence,Chizhou University,Chizhou 247000,China;School of Mathematics and Statistics,Nanning Normal University,Nanning 530100,China)

机构地区：[1]池州学院大数据和人工智能学院,安徽池州247000 [2]南宁师范大学数学与统计学院,广西南宁530100

出　　处：《南宁师范大学学报（自然科学版）》2021年第2期37-42,47,共7页Journal of Nanning Normal University：Natural Science Edition

基　　金：Supported by National Science Foundation of China(11761015);Natural Science Foundation of Guangxi(2020GXNSFAA159010).

摘　　要：研究了一类非线性奇异摄动Volterra积分微分方程.采用迎风有限差分格式离散该方程,并对其进行了最大范数下的先验误差分析.在先验误差界的基础上,利用精确解的先验界和等分标准弧长控制函数,建立了与摄动参数无关的一阶收敛速度.A nonlinear singularly perturbed Volterra integro-differential equation is studied.This equation is discretized by an upwind finite difference scheme for which a priori error analysis in the maximum norm is derived.Based on the a priori error bound,a first-order rate of convergence,independent of the perturbation parameter,is established by using the priori bounds of exact solution and equidistributing the standard arc-length monitor function.

关 键 词：奇异摄动 VOLTERRA积分微分方程 一致收敛 自适应网格方法 

分 类 号：O241.8[理学—计算数学]