关于Romberg求积法的数学实验

Mathematical experiment of Romberg's integration

在MATLAB软件环境下对Romberg求积法做了一个数学实验,通过对复化梯形求积法的计算及误差比率的分析,导出了精度更高的复化Simpson求积公式,对其进一步分析,又导出了复化Cotes求积公式,这一系列公式正是Romberg求积法。这一实验有助于学生理解Richardson外推法的精髓。

With MATLAB, a mathematical experiment on calculus of Romberg＇s integration has been done, and after calculating composite trapezoidal integration and analyzing error ratios, we obtain an Simpson＇s integration formula, which is much more precise. Through further analyzing the method above, we have got the formula of composite Cotes＇s integration, which is Romgerg＇s integration. Such an experiment is helpful for students to understand the main ideas of Richardson＇s extranolation.