Research on the double exponential transformation subroutine package
双指数变换子程序包的研究
基本信息
- 批准号:12640119
- 负责人:
- 金额:$ 2.24万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (C)
- 财政年份:2000
- 资助国家:日本
- 起止时间:2000 至 2002
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Suppose that an integral over (a, b) is given. Then it is known that, if you transform the integral using a function which maps (a, b) onto (-∽, ∽) and apply the trapezoidal rule with an mesh size to the integral after the transformation you will get a result with high precision. In 1974 H. Takahashi and M. Mori, the head investigator, found that if you choose a transformation by which the function after the transformation decays double exponentially the result will be the best, and they proposed several specific transformations useful for numerical evaluation of various kind of integrals. A formula obtained in this way is called the double exponential formula.The purpose of the present research project is to provide users with a subroutine package of the double exponential formulas. The package we developed includes subroutines for integrals over a finite interval, integrals with end point singularity, integrals of a slowly decaying function over (0, ∽), Fourier type integrals of a slowly decaying function, and it also includes automatic integrators. An automatic integrator is a subroutine that, when the user gives a function subprogram defining the integrand and an error tolerance, returns a result whose error is expected to lie in the tolerance. We prepared a manual which shows how to use the package and printed it in the report of the present research together with the entire source code written in FORTRAN.
假设给定对(a, b)的积分。由此可知,利用(a, b)映射到(-∽,∽)上的函数对积分进行变换,并对变换后的积分应用网格大小的梯形定则,可以得到精度较高的结果。1974年,首席研究员高桥(H. Takahashi)和森(M. Mori)发现,如果选择一种变换,变换后的函数以指数方式衰减两倍,结果将是最好的。他们提出了几种对各种积分的数值计算有用的具体变换。用这种方法得到的公式称为双指数公式。本研究计划的目的是为使用者提供一个二重指数公式的子程式包。我们开发的软件包包括有限区间积分子程序、端点奇点积分子程序、(0,∽)上缓慢衰减函数的积分子程序、缓慢衰减函数的傅里叶型积分子程序以及自动积分器。自动积分器是一个子例程,当用户给出定义积分器和容错值的函数子程序时,它返回一个结果,其错误预计在容错值之内。我们准备了一份说明如何使用软件包的手册,并将其与用FORTRAN编写的整个源代码一起打印在本研究报告中。
项目成果
期刊论文数量(25)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Takuya Ooura: Journal of Computational and Applied Mathematics. (印刷中).
Takuya Ooura:计算与应用数学杂志(正在出版)。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Kaname Amano: Contributions in Analytic Extension Formulas and their Applications. 15-25 (2001)
Kaname Amano:对解析扩展公式及其应用的贡献。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Saburou Saitoh: "Representations of analytic functions in terms of local values by means of the Riemann mapping function"Complex Variables. 45. 387-393 (2001)
Saburou Saitoh:“通过黎曼映射函数以局部值表示解析函数”复变量。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Takuya Ooura: "A continuous Euler transformation and its application to the Fourier transform of a slowly decaying function"Journal of Computational and Applied Mathematics. 130. 259-270 (2001)
Takuya Ooura:“连续欧拉变换及其在缓慢衰减函数的傅里叶变换中的应用”计算与应用数学杂志。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Masatake Mori: "The double exponential transformation in numerical analysis"Journal of Computational and Applied Mathematics. 127. 287-296 (2001)
Masatake Mori:“数值分析中的双指数变换”计算与应用数学杂志。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
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MORI Masatake其他文献
MORI Masatake的其他文献
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{{ truncateString('MORI Masatake', 18)}}的其他基金
Developments of applications of the double exponential transformation
双指数变换的应用进展
- 批准号:
18560063 - 财政年份:2006
- 资助金额:
$ 2.24万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Research on the double exponential formula for indefinite integrals
不定积分双指数公式的研究
- 批准号:
15607017 - 财政年份:2003
- 资助金额:
$ 2.24万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Research on visualization of the double exponential transformation
双指数变换的可视化研究
- 批准号:
09650077 - 财政年份:1997
- 资助金额:
$ 2.24万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Mathematical Research on Anomalous Diffusion Problem
反常扩散问题的数学研究
- 批准号:
06650072 - 财政年份:1994
- 资助金额:
$ 2.24万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Co-operative Research of General Purpose FORTRAN Graphic Software System for Scientific Computation
通用FORTRAN科学计算图形软件系统合作研究
- 批准号:
05302028 - 财政年份:1993
- 资助金额:
$ 2.24万 - 项目类别:
Grant-in-Aid for Co-operative Research (A)
Research on Algorithms for Numerical Computation by Supercomputer
超级计算机数值计算算法研究
- 批准号:
61540142 - 财政年份:1986
- 资助金额:
$ 2.24万 - 项目类别:
Grant-in-Aid for General Scientific Research (C)
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