NUMERICAL ANALYSIS OF A NONLINEAR SINGULARLY PERTURBED DELAY VOLTERRA INTEGRO-DIFFERENTIAL EQUATION ON AN ADAPTIVE GRID  

作　　者：Libin Liu Yanping Chen Ying Liang 

机构地区：[1]School of Mathematics and Statistics,Nanning Normal University,Nanning 530023,China [2]School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China

出　　处：《Journal of Computational Mathematics》2022年第2期258-274,共17页计算数学（英文）

基　　金：This work is supported by the State Key Program of National Natural Science Foundation of China(11931003);National Science Foundation of China(41974133,11761015,11971410);the Natural Science Foundation of Guangxi(2020GXNSFAA159010).

摘　　要：In this paper,we study a nonlinear first-order singularly perturbed Volterra integro-differential equation with delay.This equation is discretized by the backward Euler for differential part and the composite numerical quadrature formula for integral part for which both an a priori and an a posteriori error analysis in the maximum norm are derived.Based on the a priori error bound and mesh equidistribution principle,we prove that there exists a mesh gives optimal first order convergence which is robust with respect to the perturbation parameter.The a posteriori error bound is used to choose a suitable monitor function and design a corresponding adaptive grid generation algorithm.Furthermore,we extend our presented adaptive grid algorithm to a class of second-order nonlinear singularly perturbed delay differential equations.Numerical results are provided to demonstrate the effectiveness of our presented monitor function.Meanwhile,it is shown that the standard arc-length monitor function is unsuitable for this type of singularly perturbed delay differential equations with a turning point.

关 键 词：Delay Volterra integro-differential equation Singularly perturbed Error analysis Monitor function 

分 类 号：O17[理学—数学]