{"id":903,"date":"2017-12-15T16:01:29","date_gmt":"2017-12-15T21:01:29","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1013\/?p=903"},"modified":"2026-04-05T05:49:13","modified_gmt":"2026-04-05T10:49:13","slug":"2eva2015ti_t3-edp-parabolica","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/mn-2eva20\/2eva2015ti_t3-edp-parabolica\/","title":{"rendered":"2Eva2015TI_T3 EDP parab\u00f3lica"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">2da Evaluaci\u00f3n I T\u00e9rmino 2015-2016. 8\/Septiembre\/2015. ICM00158<\/h2>\n\n\n\n<p><strong>Tema 3<\/strong>. (30 puntos) Use el m\u00e9todo de diferencias progresivas para aproximar la soluci\u00f3n de la ecuaci\u00f3n diferencial parcial parab\u00f3lica<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> \\frac{\\partial u}{\\partial t} - \\frac{4}{\\pi ^2}\\frac{\\partial ^2 u}{\\partial x^2} = 0 <\/span>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><span class=\"wp-katex-eq katex-display\" data-display=\"true\"> 0 &lt; x &lt; 4<\/span>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><span class=\"wp-katex-eq katex-display\" data-display=\"true\"> t&gt;0 <\/span>\n<\/div>\n<\/div>\n\n\n\n<p>siendo:<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> u(x,0) = \\sin \\Big( \\frac{\\pi}{4}x \\Big) \\Big( 1 + 2 \\cos \\Big( \\frac{\\pi}{4}x\\Big)\\Big)<\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> 0 \\leq x \\leq 4 <\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> u(0,t) = u(4,t) = 0<\/span>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> t&gt;0 <\/span>\n\n\n\n<p>a) Use <strong>n<\/strong>=20 en el sentido de x; y <strong>m<\/strong>=10, obtenga el modelo (solo planteado).<\/p>\n\n\n\n<p>b) Aproxime la soluci\u00f3n con <strong>n<\/strong>=4, hasta 2\u0394<strong>t<\/strong>, y<\/p>\n\n\n\n<p>c) estime el error en el punto P(x<sub>1<\/sub>, t<sub>1<\/sub>)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>2da Evaluaci\u00f3n I T\u00e9rmino 2015-2016. 8\/Septiembre\/2015. ICM00158 Tema 3. (30 puntos) Use el m\u00e9todo de diferencias progresivas para aproximar la soluci\u00f3n de la ecuaci\u00f3n diferencial parcial parab\u00f3lica siendo: a) Use n=20 en el sentido de x; y m=10, obtenga el modelo (solo planteado). b) Aproxime la soluci\u00f3n con n=4, hasta 2\u0394t, y c) estime el [&hellip;]<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"wp-custom-template-entrada-mn","format":"standard","meta":{"footnotes":""},"categories":[20],"tags":[57],"class_list":["post-903","post","type-post","status-publish","format-standard","hentry","category-mn-2eva20","tag-edp"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/903","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/users\/8043"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/comments?post=903"}],"version-history":[{"count":8,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/903\/revisions"}],"predecessor-version":[{"id":17393,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/903\/revisions\/17393"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=903"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=903"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=903"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}