{"id":2142,"date":"2012-08-21T06:59:25","date_gmt":"2012-08-21T06:59:25","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=2142"},"modified":"2013-03-08T05:48:13","modified_gmt":"2013-03-08T05:48:13","slug":"resena-numerical-analysis-of-ordinary-differential-equations-in-isabellehol","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/resena-numerical-analysis-of-ordinary-differential-equations-in-isabellehol\/","title":{"rendered":"Rese\u00f1a: Numerical analysis of ordinary differential equations in Isabelle\/HOL"},"content":{"rendered":"<p>El mi\u00e9rcoles (15 de agosto de 2012) se present\u00f3 en el <a href=\"http:\/\/itp2012.cs.princeton.edu\">ITP 2012<\/a> (Interactive Theorem Proving) un trabajo de razonamiento formalizado en <a href=\"http:\/\/www.cl.cam.ac.uk\/research\/hvg\/isabelle\">Isabelle\/HOL<\/a> titulado <a href=\"http:\/\/home.in.tum.de\/~immler\/itp2012_draft.pdf\">Numerical analysis of ordinary differential equations in Isabelle\/HOL<\/a><\/p>\n<p>Sus autores son <a href=\"http:\/\/home.in.tum.de\/~immler\">Fabian Immler<\/a> y <a href=\"http:\/\/home.in.tum.de\/~hoelzl\">Johannes H\u00f6lzl<\/a> (de la <i>Technische Universit\u00e4t M\u00fcnchen<\/i>).<\/p>\n<p>El resumen del trabajo es<\/p>\n<blockquote><p>\nMany ordinary differential equations (ODEs) do not have a closed solution, therefore approximating them is an important problem in numerical analysis. This work formalizes a method to approximate solutions of ODEs in Isabelle\/HOL.<\/p>\n<p>We formalize initial value problems (IVPs) of ODEs and prove the existence of a unique solution, i.e. the Picard-Lindel\u00f6f theorem. We introduce generic one-step methods for numerical approximation of the solution and provide an analysis regarding the local and global error of one-step methods.<\/p>\n<p>We give an executable specification of the Euler method as an instance of one-step methods. With user-supplied proofs for bounds of the differential equation we can prove an explicit bound for the global error. We use arbitrary-precision floating-point numbers and also handle rounding errors when we truncate the numbers for efficiency reasons.\n<\/p><\/blockquote>\n<p>El c\u00f3digo de la formalizaci\u00f3n en Isabelle\/HOL se encuentra <a href=\"http:\/\/afp.sourceforge.net\/devel-entries\/Ordinary_Differential_Equations.shtml\">aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>El mi\u00e9rcoles (15 de agosto de 2012) se present\u00f3 en el ITP 2012 (Interactive Theorem Proving) un trabajo de razonamiento formalizado en Isabelle\/HOL titulado Numerical analysis of ordinary differential equations in Isabelle\/HOL Sus autores son Fabian Immler y Johannes H\u00f6lzl (de la Technische Universit\u00e4t M\u00fcnchen). El resumen del trabajo es Many ordinary differential equations (ODEs)&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[100],"tags":[89,144,285],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_likes_enabled":false,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/2142"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/comments?post=2142"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/2142\/revisions"}],"predecessor-version":[{"id":2790,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/2142\/revisions\/2790"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=2142"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=2142"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=2142"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}