{"id":8767,"date":"2023-01-24T14:30:40","date_gmt":"2023-01-24T19:30:40","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/analisisnumerico\/?p=8767"},"modified":"2026-01-16T09:24:27","modified_gmt":"2026-01-16T14:24:27","slug":"2eva2022paoii_t3-edp-parabolica-cos34pi","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/mn-2eva30\/2eva2022paoii_t3-edp-parabolica-cos34pi\/","title":{"rendered":"2Eva2022PAOII_T3 EDP Parab\u00f3lica con coseno 3\/4\u03c0"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">2da Evaluaci\u00f3n 2022-2023 PAO II. 24\/Enero\/2023<\/h2>\n\n\n\n<p><strong>Tema 3<\/strong>. (35 puntos) Aproxime la soluci\u00f3n a la siguiente ecuaci\u00f3n diferencial parcial parab\u00f3lica<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\">\\frac{\\partial^2 u}{\\partial x^2} = b \\frac{\\partial u}{\\partial t}<\/span>\n\n\n\n<p>Con las siguientes condiciones:<\/p>\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\">\n<p>frontera:<\/p>\n\n\n\n<p>u(0,t)=1<\/p>\n\n\n\n<p>u(1,t)=0<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p>iniciales:<\/p>\n\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> u(x,0) = \\cos \\Big( \\frac{3\u03c0}{2}x\\Big) <\/span>\n<\/div>\n<\/div>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"439\" height=\"105\" src=\"http:\/\/blog.espol.edu.ec\/algoritmos101\/files\/2017\/10\/BarraMetalica01.png\" alt=\"Barra Met\u00e1lica 01\" class=\"wp-image-13861\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image alignright size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"362\" height=\"254\" src=\"http:\/\/blog.espol.edu.ec\/algoritmos101\/files\/2023\/01\/2Eva2022PAOII_T3_EDP_Parabolica.png\" alt=\"2Eva2022PAOII_T3 EDPParab\u00f3lica\" class=\"wp-image-17519\" \/><\/figure>\n\n\n\n<p>Utilice diferencias finitas centradas para x, para t hacia adelante.<\/p>\n\n\n\n<p>a. Realice la gr\u00e1fica de malla,<\/p>\n\n\n\n<p>b. Plantee las ecuaciones para usar un m\u00e9todo num\u00e9rico en un nodo i,j<\/p>\n\n\n\n<p>c. Desarrolle y obtenga el modelo discreto para u(x<sub>i<\/sub>,t<sub>j<\/sub>) que sea de inter\u00e9s<\/p>\n\n\n\n<p>Suponga que b = 2, Aproxime la soluci\u00f3n usando tama\u00f1os de paso \u0394x = 0.2, \u0394t = \u0394x\/100.<\/p>\n\n\n\n<p>d. Realice al menos tres iteraciones en el eje tiempo.<\/p>\n\n\n\n<p>e. Estime el error de u(x<sub>i<\/sub>,t<sub>j<\/sub>), y presente observaciones sobre la convergencia del m\u00e9todo.<\/p>\n\n\n\n<p><em><strong>R\u00fabrica<\/strong><\/em>: literal a (5 puntos), literal b (5 puntos), literal c (5 puntos), literal d (15 puntos), literal e (5 puntos).<\/p>\n\n\n\n<p><strong><em>Referencia<\/em><\/strong>: [1] Chapra &amp; R. Canale (2010). M\u00e9todos Num\u00e9ricos para Ingenieros. Ejercicio 30.15 p904,<\/p>\n\n\n\n<p>[2]Solving the heat equation | DE3. 3Blue1Brown 16 Junio 2019.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Solving the heat equation | DE3\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/ToIXSwZ1pJU?start=606&feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>2da Evaluaci\u00f3n 2022-2023 PAO II. 24\/Enero\/2023 Tema 3. (35 puntos) Aproxime la soluci\u00f3n a la siguiente ecuaci\u00f3n diferencial parcial parab\u00f3lica Con las siguientes condiciones: frontera: u(0,t)=1 u(1,t)=0 iniciales: Utilice diferencias finitas centradas para x, para t hacia adelante. a. Realice la gr\u00e1fica de malla, b. Plantee las ecuaciones para usar un m\u00e9todo num\u00e9rico en un [&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":[22],"tags":[57],"class_list":["post-8767","post","type-post","status-publish","format-standard","hentry","category-mn-2eva30","tag-edp"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/8767","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=8767"}],"version-history":[{"count":6,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/8767\/revisions"}],"predecessor-version":[{"id":21033,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/8767\/revisions\/21033"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=8767"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=8767"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=8767"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}