1999 Fiscal Year Final Research Report Summary
DEVELOPMENT AND APPLICATION OF SYMPLECTIC INTEGRATOR
| Project/Area Number |
09640307
|
|---|
| 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 | NATIONAL ASTRONOMICAL OBSERVATORY |
|---|
Principal Investigator |
YOSHIDA Haruo NAO, DIVISION OF ASTROMETRY AND CELESTIAL MECHANICS, ASSOCIATE PROFESSOR, 位置天文・天体力学研究系, 助教授 (70220663)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
NAKAI Hiroshi NAO, PUBLIC RELATIONS CENTERS, RESEARCH ASSOCIATE, 天文情報公開センター, 助手 (60155653)
TANIKAWA Kiyotaka NAO, DIVISION OF THEORETICAL ASTROPHYSICS, ASSOCIATE PROFESSOR, 理論天文学研究系, 助教授 (80125210)
|
|---|
| Project Period (FY) |
1997 – 1999
|
| Keywords | Hamiltonian dynamical system / Numerical integration method / Symplectic |
|---|
| Research Abstract |
As for researches directly related to the main subject, simplistic integrators for infinite dimensional Hiamiltonian systems (partial differential equations) such as nonlinear Schrodinger equation have been developed. The first order scheme corresponds to "split-step quasi Fourier method" which has been known already. Higher order explicit integrators can be easily implemented, which enable us to compute fast and very accurately. In addition, the following results have been obtained in some related areas:
(1) A new necessary condition for integrability has been obtained which is based on differential Galois theory. This new necessary condition well justifies the efficiency of empirical singular point analysis.
(2) In a family of smooth mappings in a plane, general rule has been found for the appearance of homoclinic and heteroclinic points.
(3) A new knowledge has been obtained for the smoothness of KAM curve for the standard mapping. This is based on the analysis of multi-fractal.
|
