2002 Fiscal Year Final Research Report Summary
Research on the double exponential transformation subroutine package
| Project/Area Number |
12640119
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Tokyo Denki University (2001-2002)
Kyoto University (2000) |
|---|
Principal Investigator |
MORI Masatake Tokyo Denki University, Department of Mathematical Sciences, Professor, 理工学部, 教授 (20010936)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
OOURA Takuya Kyoto University, Research Institute for Mathematical Sciences, Research Associate, 数理解析研究所, 助手 (50324710)
|
|---|
| Project Period (FY) |
2000 – 2002
|
| Keywords | double exponential transformation / numerical integration / variable transformation / subroutine package |
|---|
| Research Abstract |
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.
|
