{"created":"2023-06-20T15:10:27.064694+00:00","id":6621,"links":{},"metadata":{"_buckets":{"deposit":"90d85aa1-f9d9-49c5-bdb3-e5ef87882341"},"_deposit":{"created_by":3,"id":"6621","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"6621"},"status":"published"},"_oai":{"id":"oai:ynu.repo.nii.ac.jp:00006621","sets":["616:627:643"]},"author_link":["29459"],"item_6_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"1977","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"2","bibliographicPageEnd":"189","bibliographicPageStart":"183","bibliographicVolumeNumber":"25","bibliographic_titles":[{"bibliographic_title":"Yokohama Mathematical Journal = 横濱市立大學紀要. D部門, 数学"}]}]},"item_6_description_17":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_6_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"In this paper we will discuss methods for the numerical solution of a single first-order ordinary differential equation ＄￥frac{dy}{dx}=f(x, y)￥equiv￥frac{Q(x,y)}{P(x,y)}＄ with the initial condition ＄y(a)=b＄ . To seek the solution, we often use Runge-Kutta method provided that ＄f(x, y)＄ is continuous and satisfies Lipschitz condition ＄|f(x, y_{1})-f(x, y_{2})|￥leqq M|y_{1}-y_{2}|＄ . If ＄P(x_{0}, y_{0})=0＄ and ＄Q(x_{0}, y_{0})￥neq 0＄ , then ＄ dyldx=￥infty＄ , therefore we can not use Runge-Kutta method in the neighbourhood of ＄(x_{0}, y_{0})＄ . Nevertheless, there often exists the solution. (ex. 1) In this case, putting ＄g(x, y)=￥frac{P(x,y)}{Q(x,y)}＄ ＄g(x, y)＄ often satisfies Lipschitz condition ＄|g(x_{1}, y)-g(x_{2}, y)|￥leqq M^{￥prime}|x_{1}-x_{2}|＄ in the neighbourhood of ＄(x_{0}, y_{0})＄ . Therefore, when we use Runge-kutta method provided with ＄P(x, y)^{2}+Q(x, y)^{2}￥neq 0＄ , if ＄|P(x, y)|￥geqq|Q(x, y)|＄ , we treat ＄y＄ as the function of the independent variable ＄x＄ , if ＄|P(x, y)|<|Q(x, y)|＄ , we treat ＄x＄ as the function of the independent variable ＄y＄ , that is, if ＄|￥frac{dy}{dx}|￥leqq 1＄ , then ￥frac{dy}{dx}=￥frac{Q(X_{1}y)}{P(X_{1}y)}＄ , and if ＄|￥frac{dy}{dx}|>1＄ , then ＄￥frac{dx}{dy}=￥frac{P(x,y)}{Q(X_{1}y)}＄ , then, as ＄|dy/dx|＄ and ＄|dx/dy|＄ are both smaller than 1, the error of the increment will be smaller. If ＄P(x_{0}, y_{0})^{2}+Q(x_{0}, y_{0})^{2}=0＄ , we must stop pursuing the solution at ＄(x_{0}, y_{0})＄ as ＄(x_{0}, y_{0})＄ is a singular point. (ex. ＄6￥sim ex＄ . ＄11＄ ) Furthermore, if we can find proper continuations between dyldx and dxldy, we can even pursue closed curves. (ex. 1)","subitem_description_type":"Abstract"}]},"item_6_publisher_35":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"Yokohama City University"}]},"item_6_source_id_11":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA0089285X","subitem_source_identifier_type":"NCID"}]},"item_6_source_id_9":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"00440523","subitem_source_identifier_type":"ISSN"}]},"item_6_text_4":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"Department of Mathematics, Japan Women's University, Mejirodai, Bunkyo-ku, Tokyo, Japan"}]},"item_6_version_type_18":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Kaizuka, Tetsu"}],"nameIdentifiers":[{"nameIdentifier":"29459","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2016-09-26"}],"displaytype":"detail","filename":"YMJ_25_N2_1977_183-189.pdf","filesize":[{"value":"380.7 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"YMJ_25_N2_1977_183-189.pdf","url":"https://ynu.repo.nii.ac.jp/record/6621/files/YMJ_25_N2_1977_183-189.pdf"},"version_id":"04b34d23-d877-4548-b6de-4a5f17f44e66"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"A REMARK ON THE NUMERICAL SOLUTION OF A SINGLE FIRST-ORDER ORDINARY DIFFERENTIAL EQUATION","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"A REMARK ON THE NUMERICAL SOLUTION OF A SINGLE FIRST-ORDER ORDINARY DIFFERENTIAL EQUATION"}]},"item_type_id":"6","owner":"3","path":["643"],"pubdate":{"attribute_name":"公開日","attribute_value":"2009-12-15"},"publish_date":"2009-12-15","publish_status":"0","recid":"6621","relation_version_is_last":true,"title":["A REMARK ON THE NUMERICAL SOLUTION OF A SINGLE FIRST-ORDER ORDINARY DIFFERENTIAL EQUATION"],"weko_creator_id":"3","weko_shared_id":3},"updated":"2023-06-20T18:38:38.495369+00:00"}