求解非线性脉冲延迟微分方程的高阶数值方法  

A High Order Numerical Method for Solving Nonlinear Impulsive Delay Differential Equations

作　　者：龙滔 余越昕 LONG Tao;YU Yuexin(School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,China)

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《应用数学》2021年第4期885-893,共9页Mathematica Applicata

基　　金：国家自然科学基金(11571291);湖南省教育厅重点项目(20A484)。

摘　　要：针对一类非线性脉冲延迟微分方程,首先将其转化为等价的积分方程,然后利用修正的block-by-block方法对其离散化,得到了求解问题的高阶数值方法.最后利用数学归纳法证明了该数值方法是4阶收敛的,数值试验的结果验证了所获理论的正确性.For a class of nonlinear impulsive delay differential equation, firstly, it is transformed into an equivalent integral equation, and then the modified block-by-block method is used to discretize the equation, and a high order numerical method for solving the problem is obtained. Finally, we prove that the method is convergent of the order 4 by mathematical induction. Numerical experiments verify the correctness of the theoretical results.

关 键 词：脉冲延迟微分方程 高阶数值方法 block-by-block方法 收敛性 

分 类 号：O241.81[理学—计算数学]