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Research on visualization of the double exponential transformation

双指数变换的可视化研究

基本信息

批准号：
09650077
负责人：
MORI Masatake
金额：
$ 1.92万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09650077/
关键词：
numerical integration double exponential transformation double exponential formula complex function theory characteristic function of the error visualization computer graphics Sinc近似

项目摘要

The head investigator arid others have proposed a family of efficent formulas for numerical integration called the double exponential formula. On the other hand, the error of numerical integration can be expressed in terms of a complex integral of a product of the integrand and a function called the characteristic function of the error. In this research we developed a system which computes the characteristic function of the error and gives its contour map on a graphic display. If we.. use this system we can estimate the error of numerical integration by the double exponential formula easily and accurately.The head investigator and opthers had already written several programs which individually compute the characteristic function of the error of sonic particular integral and give its contour map. In the present research we treated the characteristic function in a unified way and developed a system which gives the contour map automatically if the user specifies the parameters such as the type of the integral, the interval of integration, etc. Also in this system we included the*Ooura's formula which compute efficiently Fourier type integrals. Furthermore, we developed a system which ti-eats Newton-Cotes formulas and Gauss type formulas. These programs are written in DIGITAL Visual Fortran, and run on a Windows 95 personal computer system.Finally we developed a system to specify the parameters through several input windows which runs on Microsoft Visual Basic. We wrote a manual to use this system and included it in the report of the present research together with the entire source. code.

首席研究员和其他人提出了一组有效的数值积分公式，称为双指数公式。另一方面，数值积分的误差可以用被积函数与误差特征函数乘积的复积分来表示。在本研究中，我们开发了一个计算误差特征函数并在图形显示器上给出其等高线图的系统。如果我们. .利用该系统可以方便、准确地估计用双指数公式进行数值积分的误差。课题组组长等已经编写了几个程序，分别计算了声波特积分误差的特征函数，并给出了其等值线图。本文对特征函数进行了统一的处理，开发了一种可以在用户指定积分类型、积分区间等参数时自动给出等高线图的系统。在这个系统中，我们还包含了* oura公式，它可以有效地计算傅里叶型积分。此外，我们还开发了一个不使用牛顿-柯茨公式和高斯型公式的系统。这些程序是用DIGITAL Visual Fortran语言编写的，在Windows 95个人电脑系统上运行。最后在Microsoft Visual Basic上开发了一个通过多个输入窗口来指定参数的系统。我们编写了使用该系统的手册，并将其与整个源代码一起包含在本研究的报告中。代码。