セキネ　コウタ   関根　晃太    所属   千葉工業大学  情報変革科学部 情報工学科    千葉工業大学  情報科学研究科 情報科学専攻    職種   准教授
言語種別	英語
発行・発表の年月	2021
形態種別	学術雑誌
査読	査読あり
招待論文	招待あり
標題	Numerical verification methods for a system of elliptic PDEs, and their software library
執筆形態	共著
掲載誌名	Nonlinear Theory and Its Applications, IEICE
掲載区分	国外
出版社・発行元	Institute of Electronics, Information and Communications Engineers ({IEICE})
巻・号・頁	12(1),pp.41-74
著者・共著者	Kouta Sekine, Mitsuhiro T. Nakao, Shin'ichi Oishi
概要	Since the numerical verification method for solving boundary value problems for elliptic partial differential equations (PDEs) was first developed in 1988, many methods have been devised. In this paper, existing verification methods are reformulated using a convergence theorem for simplified Newton-like methods in the direct product space V-h x V-perpendicular to of a computable finite-dimensional space V-h and its orthogonal complement space V-perpendicular to. Additionally, the Verified Computation for PDEs (VCP) library is provided, which is a software library written in the C++ programming language. The VCP library is introduced as a software library for numerical verification methods of solutions to PDEs. Finally, numerical examples are presented using the reformulated verification methods and VCP library.
DOI	10.1587/nolta.12.41
ISSN	2185-4106