Q. Sheng 教授 数値解析 講演会

応用数理学会会員の皆様へ.
このたび，数値解析の講演会を開催いたします．
DATE: Thursday, May 28th

TIME: 10:40 — 12:00 AM (JST)

VENUE: Room A801, 8F, Science Complex A, Aobayama Campus, Tohoku University (Map: https://www.tohoku.ac.jp/map/en/?f=AY_H02)

SPEAKER: Qin Sheng (Tim) Department of Mathematics and Center for Astrophysics, Space Physics and Engineering Research, Baylor University, Texas, USA (currently visiting the University of Tokyo as an NSF/JSPS scholar)

TITLE: From Suzuki to Kawarada: Advances in the Splitting Methods for Solving Differential Equations

ABSTRACT: Two interesting topics will be discussed today. First, recent advancements in exponential (LOD) and non-exponential (ADI) methods, to which Professor Masuo Suzuki has made significant contributions, will be reviewed. Second, the latest decomposition strategies targeting certain nonlinear models, such as the Hideo Kawarada partial differential equation arising in combustion and cell-biological modeling and computations, will be introduced. The latter approach leads to intercardinal schemes that provide highly accurate and effective numerical approximations to the underlying problems for realistic engineering and physical applications.

A detailed numerical analysis will be presented to ensure that the implicit computational schemes are stable, convergent, and efficient, while preserving key physical properties such as positivity and monotonicity. The orders of accuracy of the algorithms are shown to be highly nonlinear, as illustrated through generalized Milne devices. Three-dimensional simulation examples of the solution procedures will be presented, and extensions for solutions of Helmholtz, Schrödinger and Black-Scholes equations will be outlined.

Students at all levels are warmly encouraged to attend and participate in the discussion.