摘要
构造了求解一类延迟二阶线性微分方程的两点边值问题的二阶有限体积法.对求解区间均匀离散,采用线性离散插值方法在每个小区间上对方程进行数值积分,得出相应的数值方法.误差分析显示,在离散H-1半范数、L-2范数以及最大范数下,数值解关于步长都是二阶收敛的.并且,有限的数值结果验证了该数值方法的有效性.
A two-order finite volume method was presented for a class of two-order linear differential equations with delay. Firstly,the interval was divided into a set of small intervals. Then,the finite volume scheme was obtained by integrating the equation on each tiny interval and using the linear discrete interpolation method. Moreover,the errors of the numerical solution,such as discrete H-1 semi-norm error,L-2 norm error and maximum norm error,were analyzed,which showed the finite volume scheme is two-order convergent. Finally,numerical results verified the validity of the presented scheme.
作者
冯和英
尹锋霖
常鸿
Feng Heying;Yin Fenglin;Chang Hong(Hunan Provincial Key Laboratory of Heahh Maintenance for Mechanical Equipment, Hunan University of Science and Technology, Xiangtan 411201, China;School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, China)
出处
《湖南科技大学学报（自然科学版）》
CAS
北大核心
2018年第1期114-124,共11页
Journal of Hunan University of Science And Technology：Natural Science Edition
基金
国家自然科学基金资助项目(51476052)
湖南省教育厅资助项目(14C0433)
研究生创新基金项目(S140034,CX2017B617)
关键词
有限体积法
两点边值问题
均匀网格
finite-volume method
two-point boundary value problems
uniform grid
