典型文献
NUMERICAL ANALYSIS OF A NONLINEAR SINGULARLY PERTURBED DELAY VOLTERRA INTEGRO-DIFFERENTIAL EQUATION ON AN ADAPTIVE GRID
文献摘要：
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 perturba-tion 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 per-turbed delay differential equations.Numerical results are provided to demonstrate the effectiveness of our presented monitor function.Meanwhile,it is shown that the stan-dard arc-length monitor function is unsuitable for this type of singularly perturbed delay differential equations with a turning point.
文献关键词：
中图分类号：
作者姓名：
Libin Liu;Yanping Chen;Ying Liang
作者机构：
School of Mathematics and Statistics,Nanning Normal University,Nanning 530023,China;School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China
文献出处：
引用格式：
[1]Libin Liu;Yanping Chen;Ying Liang-.NUMERICAL ANALYSIS OF A NONLINEAR SINGULARLY PERTURBED DELAY VOLTERRA INTEGRO-DIFFERENTIAL EQUATION ON AN ADAPTIVE GRID)[J].计算数学（英文版）,2022(02):258-274
A类：
NUMERICAL,ANALYSIS,NONLINEAR,SINGULARLY,PERTURBED,VOLTERRA,INTEGRO,DIFFERENTIAL,EQUATION,ADAPTIVE,singularly,equidistribution
B类：
OF,DELAY,GRID,In,this,paper,we,study,nonlinear,first,order,perturbed,Volterra,integro,differential,delay,This,discretized,by,backward,Euler,part,composite,numerical,quadrature,formula,integral,which,both,priori,posteriori,error,analysis,maximum,norm,are,derived,Based,bound,mesh,principle,prove,that,there,exists,gives,optimal,convergence,robust,respect,perturba,parameter,used,choose,monitor,function,design,corresponding,adaptive,grid,generation,algorithm,Furthermore,extend,our,presented,class,second,equations,Numerical,results,provided,demonstrate,effectiveness,Meanwhile,shown,stan,dard,arc,length,unsuitable,type,turning,point
AB值：
0.496167
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