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Numerical Analysis Seminar
Seminar information archive ～04/05｜Next seminar｜Future seminars 04/06～
| Date, time & place | Tuesday 16:30 - 18:00 002Room #002 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Norikazu Saito, Takahito Kashiwabara |
2026/05/26
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Qin Sheng (Baylor University)
Advances in Splitting: Intercardinal Approaches to Nonlinear Hideo Kawarada Equations
(English)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Qin Sheng (Baylor University)
Advances in Splitting: Intercardinal Approaches to Nonlinear Hideo Kawarada Equations
(English)
[ Abstract ]
This presentation addresses two main issues. First, we shall discuss recent advancements in both exponential and non-exponential splitting methods, with particular emphasis on their stability, accuracy and global error estimates. Second, we shall introduce a new splitting configuration for solving nonlinear Hideo Kawarada equations with mixed derivative terms. This approach leads to intercardinal splitting finite-difference schemes that provide efficient and accurate numerical approximations of the underlying solutions.
We shall further demonstrate that the resulting implicit methods are numerically stable, convergent, and efficient, while preserving key physical properties such as the positivity and monotonicity. The dynamic orders of accuracy of the proposed algorithms will be illustrated using generalized Milne devices. Simulation examples of the solution procedure will be presented and investigated, and several open problems will also be outlined.
[ Reference URL ]This presentation addresses two main issues. First, we shall discuss recent advancements in both exponential and non-exponential splitting methods, with particular emphasis on their stability, accuracy and global error estimates. Second, we shall introduce a new splitting configuration for solving nonlinear Hideo Kawarada equations with mixed derivative terms. This approach leads to intercardinal splitting finite-difference schemes that provide efficient and accurate numerical approximations of the underlying solutions.
We shall further demonstrate that the resulting implicit methods are numerically stable, convergent, and efficient, while preserving key physical properties such as the positivity and monotonicity. The dynamic orders of accuracy of the proposed algorithms will be illustrated using generalized Milne devices. Simulation examples of the solution procedure will be presented and investigated, and several open problems will also be outlined.
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
