2014 Fiscal Year Final Research Report

Library for Validated Computation of Differential Equations

Research Project

Project/Area Number	24540115
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Multi-year Fund
Section	一般
Research Field	General mathematics (including Probability theory/Statistical mathematics)
Research Institution	The University of Electro-Communications
Principal Investigator	YAMAMOTO Nobito 電気通信大学, 情報理工学(系)研究科, 教授 (30210545)
Project Period (FY)	2012-04-01 – 2015-03-31
Keywords	精度保証 / 偏微分方程式 / 常微分方程式 / 多倍長演算
Outline of Final Research Achievements	We have developed the following. (1) Numerical verification methods for norm estimation of invers differential operators w.r.t. PDEs. (2) Validated methods of constructing Lyapunov functions w.r.t. ODEs (3) A library named LILIB for usage of interval multi precision arithmetic with guaranteed accuracy.
Free Research Field	数値解析、精度保証付き数理計算