论数值积分的方法及其在MATLAB中的实现

The theory and its realization in the matlab numerical integral method
Abstract:This paper introduces several methods of numerical integration. A simple formula of rectangular, trapezoidal formula relative to the Simpson formula of higher algebraic accuracy, and finally leads to the Newton Cotes formula. To improve the precision, the complex of the quadrature formula (including Romberg integral algorithm), Gauss integral algorithm. This paper introduces the Newton Cotes formula, Romberg algorithm and Gauss integral formula. Then the precision and accuracy of numerical comparison of these theory, using MATLAB programming analysis calculation method and the advantages and disadvantages of each comparison. The significance embodies a numerical integral method in MATLAB for solving practical problems.
Key words:Numerical integration;Romberg integral algorithm;Newton-Cotes formula; Gauss integral algorithm; The program of MATLAB

1.数值积分概述    3
1.1数值积分的基本思想    3
1.2代数精度    5
2.数值积分的几种方法    7

2.1牛顿-柯特斯公式    7
2.2复化数值求积公式    10
2.3龙贝格算法    11
2.4高斯-勒让德求积公式    13
3.数值积分法的实例    16
3.1几种数值积分法的例子    16
3.2数值分析的方法在实际中的应用    16
4.总结    18

MATLAB的出现就很大程度上的解决了这类问题，MATLAB本以为矩阵实验室，依托矩阵进行大规模，高精度数组数据运算，在解决复杂工程问题时，MATLAB有精度较高，计算快的特点。用户可根据自己所解决问题的特点进行一定改进，这都使MATLAB成为优秀的求解数值积分的工具。现如今，MATLAB已占到了数值积分市场的主要位置，越来越顺应社会多功能需求的潮流。因此，数值积分在MATLAB上的实现也越来越重要。 论数值积分的方法及其在MATLAB中的实现:http://www.lwfree.cn/shuxue/20190730/36454.html
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