Analysis Seminar

主講者: 1.Prof. Hitoshi Imai 今井 仁司 教授 (Tokushima University) 2.Prof. Yuusuke Iso 磯 祐介 教授 (Kyoto University)
講題: 1. Numerical experiments for investigation of the property of the functions 2. Does stability estimate in the finite difference method for PDE's guarantee stability of numerical solutions?
時間: 2013-03-18 (Mon.)  10:00 - 13:00
地點: 數學所 617 研討室 (台大院區)
Abstract: 1.We present numerical methods to investigate the property of the functions. Two kinds of numerical computation are carried out by using data generated from the function. First one is interpolation, and second one is direct numerical simulation of the Cauchy problem for the Laplace equation. Some numerical results suggest that our methods are useful for the distinction between the smooth functions and the analytic functions. This work is a joint work with Prof. Hideo Sakaguchi(Tokushima Univ.) 2.We consider the finite difference method(FDM) applied to well-posed evolutional problems for linear PDE's. Stability is one of the most important concepts in the analysis for FDM, and we believe it to ensure stable numerical solutions. We give a mathematical model for accumulation of the rounding errors, and we show some numerical examples that numerical solutions diverge under the stability condition. We also mention the meaning the Courant-Friedrichs-Lewy condition. This work is a joint work with Prof. Hiroshi Fujiwara(Kyoto Univ.).
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