1数值计算基于物理研究摘要：本文首先简单地介绍了数值积分的基本思想,然后阐述了复合梯形公式､Richardson 外推算法及 Romberg 算法,最后给出了实现 Romberg 算法的通用函数｡Rombe 求积方法是以复合梯形公式为基础,将 Richardson 外推法与 Euler-Maclauri 求和公式相结合而导出的数值积分公式｡Romberg 求积方法的优点是计算有规律,只要计算梯形公式,然后线性组合,即可构造高精度的公式｡关键词：数值积分；复合梯形公式；Richardson 外推算法；Romberg 算法；复合梯形公式abstract In this paper, the basic idea of numerical integration is briefly introduced, then the composite Trapezoidal rule Richardson extrapolation algorithm and ｡Romberg algorithm are elaborated. At last, the universal function Rombe integration method for Romberg algorithm is given, which is based on composite Trapezoidal rule and combines Richardson extrapolation with Euler-Maclauri summation formula. Romberg integration method has the advantage of regular calculation, and high precision formula can be constructed only by calculating Trapezoidal rule and then linear combination. Key words: numerical integration; Compound Trapezoidal rule; Richardson extrapolation algorithm; Romberg algorithm; Composite Trapezoidal rule2目录引言..............................................................................................................................................- 3 -1.Romberg 求积方法的基本原理及思想方法............................................................................- 3 -1.1 复合梯形公式................................................................................................................- 3 -1.2Euler-Maclaurin 求和公式...............................................................................................- 5 -1.3Richardson 外推定理......................................................................................................- 5 -1.4 Romberg 求积方法.....................
