一种改进的奇异两点边值问题的三次B样条数值解法  

A Modified Cubic B-Spline Numerical Solution of Singular Two-Point Boundary Value Problems

作　　者：张晓磊[1] 杨晶晶 王予暤 龚佃选 Zhang Xiaolei;Yang Jingjing;Wang Yuhao;Gong Dianxuan(School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018;College of Science,North China University of Science and Technology,Tangshan 063210)

机构地区：[1]浙江工商大学统计与数学学院,杭州310018 [2]华北理工大学理学院,唐山063210

出　　处：《系统科学与数学》2024年第5期1292-1302,共11页Journal of Systems Science and Mathematical Sciences

基　　金：浙江省自然科学基金项目(LY19A010003)资助课题.

摘　　要：奇异两点边值问题常广泛出现于应用数学和物理学中,这是一个经典问题并且许多学者都对此问题进行了大量的研究工作.文章提出了利用三次B样条函数来计算一类奇异两点边值问题的数值解的方法.该方法基于三次B样条函数在节点处的二阶导数值线性组合去逼近给定函数的二阶导数值,使其具有超收敛性.文章的三次B样条函数在节点处逼近给定函数的一阶导数值和二阶导数值都具有超收敛性,从而该数值格式的逼近阶达到四阶.与其他已有方法相比,数值实验表明该方法是有效可行的.Singular two-point boundary value problems arise in a variety of applied mathematics and physics.It is a classical problem and many researchers have done a lot of research work on this issue.In this paper,we apply cubic B-spline to explore the numerical solutions of a class of singular two-point boundary value problems.The paper method is primarily based on the super convergence in approximating second-order derivative values at the knots by the combination of second-order derivative values of cubic B-spline.The paper proposed cubic B-spline possesses super convergence in approximating the first-order derivative/second-order derivative of given function and thus the approximation order of our method reaches fourth order.Some numerical experiments are provided to demonstrate the effectiveness of our method compared to the other existing methods.

关 键 词：奇异两点边值问题 数值解 三次B-样条 超收敛 

分 类 号：O241.82[理学—计算数学]