1998 Fiscal Year Final Research Report Summary
Numerical Analysis of Evolution Systems
| Project/Area Number |
08304016
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (A)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | NAGOYA UNIVERSITY |
|---|
Principal Investigator |
MITSUI Taketomo Grad.Sch.of Human Informatics, Nagoya Univ., Professor, 大学院・人間情報学研究科, 教授 (50027380)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
MUROTA Kazuo Kyoto Univ., Prof., 数理解析研究所, 教授 (50134466)
NAKASHIMA Masaharu Kagoshima Univ., Prof., 理学部, 教授 (40041230)
NAKAO Mitsuhiro Kyushu Univ., Prof., 数理学研究科, 教授 (10136418)
SHINOHARA Yoshitane Tokushima Univ., Prof., 工学部, 教授 (40035803)
KOTO Toshiyuki Univ.of Electro-Communications, Assoc.Prof., 電気通信学部, 助教授 (30234793)
|
|---|
| Project Period (FY) |
1996 – 1998
|
| Keywords | Mathematical modelling / Evolution systems / Differential equations / Numerical solutions / Discretization / Stability / Computational mathematical sciences |
|---|
| Research Abstract |
The project. has been carried out., aiming to study the evolution systems in both analytical and numerical points of view. The systems are known to appear in mathematical modelling of broad area in science and engineering. The results obtained by the listed investigators as well as by their collaborators are as follows.
Discrete variable methods for systems with time-delay or randomness. Linear and nonlinear analysis has been done for their stability. Physical applications are also considered.
Long-term integration of Hamiltonian systems. Algebraic correspondence between Hamilton systems and their symplectic numerical integrators is unveiled. Symplecticness and the conservative quantities are also studied.
Self-validating numerical solution of differential equations. The solution of parabolic partial differential equations is successfully achieved. Ordinary differential equation case is also tackled.
Parallelism for evolution systems. Across-the-step and across-the-method parallelism have been studied with analysis of convergence.
Stable and high-performance numerical methods. Various modification have been introduced for Runge-Kutta schemes to attain the purpose. Sonic of them have been tested numerically.
The achievement, of the research work has been or is to be published in many articles, a part. of which is listed in the following page.
|
