基于块脉冲函数求解第一类Volterra积分方程的数值分析（英文）  

The numerical analysis of Volterra integral equations of the first kind by block-pulse functions

作　　者：张宇佳 张婷婷 梁慧[1] ZHANG Yujia;ZHANG Tingting;LIANG Hui(School of Mathematical Sciences, Heilongjiang University, Harbin 150080, China)

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》2019年第2期172-177,共6页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the Research Fund of Heilongjiang Provincial Education Department for the Academic Backbone of the Excellent Young People(1254G044)

摘　　要：本文主要基于块脉冲函数求解第一类Volterra积分方程。介绍了块脉冲函数的定义和性质,基于块脉冲函数的性质及其积分算子矩阵数值求解第一类Volterra积分方程,给出了相应的数值格式,证明数值解的存在唯一性,以及相应数值方法的1阶收敛性。数值算例验证了理论结果的正确性。It mainly focuses on how to solve Volterra integral equations of the first kind based on block-pulse functions. The definition and properties of block pulse functions are introduced briefly. Based on the properties of block pulse functions and their operational matrix of integration, Volterra integral equation of the first kind is solved numerically, and the corresponding numerical scheme is given. The existence and uniqueness of the approximate solution are proved. The convergence with order 1 of the corresponding numerical method is proved in detail. Some numerical experiments are given to illustrate the theoretical results.

关 键 词：VOLTERRA积分方程 第一类 块脉冲函数 收敛性 

分 类 号：O241.83[理学—计算数学]