奇异摄动Volterra积分微分方程参数一致的数值方法  

A Parameter-Uniform Numerical Method for a Singularly Perturbed Volterra Integro-Differential Equation

作　　者：刘利斌 廖仪戈 隆广庆 Liu Libin;Liao Yige;Long Guangqing(Center for Applied Mathematics of Guangci,Nanning Normal University,Nanning 530100)

机构地区：[1]南宁师范大学应用数学中心,南宁530100

出　　处：《数学物理学报(A辑)》2025年第2期576-583,共8页Acta Mathematica Scientia

基　　金：国家自然科学基金(12361087,12261062)。

摘　　要：针对一类奇异摄动Volterra积分微分方程,在Vulanovic-Bakhvalov网格上构造了一个一阶参数一致收敛的有限差分格式.进一步,基于Richardson外推技术,将数值格式的收敛阶从O(N^(-1))提高到O(N^(-2)),其中N是网格剖分数.最后,数值实验证明了数值方法的有效性.A singularly perturbed Volterra integro-differential equation is considered.The problem is discretized by using a simple first-order finite difference scheme on a Vulanovic-Bakhvalov mesh,the accuracy of which is first-order uniformly convergent with respect to the perturbation parameter.Furthermore,based on the Richardson extrapolation technique,the e-uniform accuracy of the presented approximation scheme can be improved from O(N^(-1))to O(N^(-2)),where N is the number of mesh intervals.Finally,the theoretical finds are illustrated by two numerical experiments.

关 键 词：奇异摄动 VOLTERRA积分微分方程 RICHARDSON外推 Vulanovic-Bakhvalov网格 

分 类 号：O241.8[理学—计算数学]