首都师范大学学报（自然科学版）2025，Vol.46Issue(4)：37-44,8.DOI:10.19789/j.1004-9398.2025.04.005
双辛普森递推算法的研究与实现
Research and implementation of double Simpson's recursive algorithm
摘要
Abstract
Aiming at the problems of slow convergence speed and insufficient node utilization of the double trapezoidal recursion algorithm,a method with higher accuracy and faster convergence of the algorithm—double Simpson recursion algorithm is proposed,from which the double Simpson recursion formula of double integration is halved in the interval under a rectangular region,and the specific algorithm implementation is given.The algorithm is applied to calculate the double integration problem of continuous functions under rectangular region and irregular region,respectively.By calculating the area of the upper semi-ellipsoidal surface,it is concluded that the double Simpson recursion algorithm has faster convergence speed,higher calculation accuracy and shorter program calculation time than the double trapezoidal recursion algorithm.Finally,by solving the initial value problem of the chord vibration equation,the application of the double Simpson recursion algorithm in the double integral calculation under the general integration region is given,which shows that the applicability of the double Simpson recursion algorithm is stronger,and the application of the algorithm in the field of partial differential equations is further explained.关键词
二重数值积分/双梯形递推算法/双辛普森递推方法/弦振动方程Key words
double numerical integration/double trapezoidal recursion method/double Simpsons recursive method/string vibration equation分类
信息技术与安全科学引用本文复制引用
刘海峰,贾旭康,樊定成,梁星亮..双辛普森递推算法的研究与实现[J].首都师范大学学报（自然科学版）,2025,46(4):37-44,8.基金项目
国家自然科学基金项目(12001345) （12001345）
陕西科技大学大学生创新创业训练计划项目(2023005) （2023005）
