A Simple Example for Linear Partial Differential Equations and Its Solution Using the Method of Separation of Variables

Pole DC	Wartość	Język
dc.contributor.author	Otsuki, Sora	-
dc.contributor.author	Kawamoto, Pauline N.	-
dc.contributor.author	Yamazaki, Hiroshi	-
dc.date.accessioned	2019-05-21T07:18:00Z	-
dc.date.available	2019-05-21T07:18:00Z	-
dc.date.issued	2019	-
dc.identifier.citation	Formalized Mathematics, Volume 27, Issue 1, Pages 25-34	-
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/7837	-
dc.description.abstract	In this article, we formalized in Mizar [4], [1] simple partial differential equations. In the first section, we formalized partial differentiability and partial derivative. The next section contains the method of separation of variables for one-dimensional wave equation. In the last section, we formalized the superposition principle.We referred to [6], [3], [5] and [9] in this formalization.	-
dc.language.iso	en	-
dc.publisher	DeGruyter Open	-
dc.subject	partial differential equations	-
dc.subject	separation of variables	-
dc.subject	superposition principle	-
dc.title	A Simple Example for Linear Partial Differential Equations and Its Solution Using the Method of Separation of Variables	-
dc.type	Article	-
dc.identifier.doi	10.2478/forma-2019-0003	-
dc.description.Affiliation	Sora Otsuki - Shinshu University, Nagano, Japan	-
dc.description.Affiliation	Pauline N. Kawamoto - Shinshu University, Nagano, Japan	-
dc.description.Affiliation	Hiroshi Yamazaki - Shinshu University, Nagano, Japan	-
dc.description.references	Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pak. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.	-
dc.description.references	Noboru Endou, Hiroyuki Okazaki, and Yasunari Shidama. Higher-order partial differentiation. Formalized Mathematics, 20(2):113–124, 2012. doi:10.2478/v10037-012-0015-z.	-
dc.description.references	John Fritz. Nonlinear Wave Equations, Formulation of Singularities. American Mathematical Society, 1990. ISBN 978-0-8218-7001-3.	-
dc.description.references	Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1.	-
dc.description.references	Mitsuhiro Nakao. Bibun-sekibun-gaku (Japanese). Kindai-kagaku-sha, pages 52–53, 1992.	-
dc.description.references	Ian Naismith Sneddon. Elements of Partial Differential Equations. Tokyo McGraw-Hill Kogakusha, pages 209–273, 1957.	-
dc.description.references	Hiroshi Yamazaki, Yoshinori Fujisawa, and Yatsuka Nakamura. On replace function and swap function for finite sequences. Formalized Mathematics, 9(3):471–474, 2001.	-
dc.description.references	Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255–263, 1998.	-
dc.description.references	Kentaro Yano. Kaiseki-gaku-gairon (Japanese). Shokabo Co., Ltd., 1982.	-
dc.identifier.eissn	1898-9934	-
dc.description.volume	27	-
dc.description.issue	1	-
dc.description.firstpage	25	-
dc.description.lastpage	34	-
dc.identifier.citation2	Formalized Mathematics	-
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