比例延迟微分方程均匀网格的BDF方法的收敛性及稳定性（英文）  

Convergence and stability of backward differential formulas on uniform meshes for pantograph differential equation

作　　者：刘洋[1] 何春燕[1] 梁慧[1] 闫晗 

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2017年第4期404-411,共8页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the Natural Science Foundation of Heilongjiang Province(A201211);the University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province(UNPYSCT-2016020);the Research Fund of the Heilongjiang Provincial Education Department for the Academic Backbone of the Excellent Young People(1254G044);the Heilongjiang University Science Funds for Distinguished Young Scholars(JCL201303)

摘　　要：研究在均匀网格下,比例延迟微分方程向后微分公式的收敛性及稳定性。在均匀网格下,将向后微分公式与线性插值相结合来求解比例延迟微分方程,给出相应的差分格式,证明该差分格式数值解的收敛阶为1;分析比例延迟微分方程向后微分公式的渐近稳定性;数值算例验证了理论结果。The convergence and stability of backward differential formulas on uniform meshes for panto- graph differential equations are dealt with. The backward differential formula （BDF） combined with a lin- ear interpolation on uniform meshes is presented to solve pantograph differential equations. It is proved that the numerical solution BDF is investigated. Some convergent to the exact solution with order 1. The asymptotic stability of the numerical experiments are given to illustrate the theoretical results obtained.

关 键 词：比例延迟微分方程 向后微分公式 线性插值 收敛性 渐近稳定性 

分 类 号：O241.8[理学—计算数学]