{"id":9030,"date":"2023-08-31T08:30:43","date_gmt":"2023-08-31T13:30:43","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/analisisnumerico\/?p=9030"},"modified":"2025-12-19T06:44:58","modified_gmt":"2025-12-19T11:44:58","slug":"2eva2023paoi_t3-edp-eliptica-placa-rectangular-frontera-variable","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/mn-2eva30\/2eva2023paoi_t3-edp-eliptica-placa-rectangular-frontera-variable\/","title":{"rendered":"2Eva2023PAOI_T3 EDP el\u00edptica, placa rectangular con frontera variable"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">2da Evaluaci\u00f3n 2023-2024 PAO I. 29\/Agosto\/2023<\/h2>\n\n\n\n<p><strong>Tema 3<\/strong> (35 puntos) Aproxime la soluci\u00f3n de la Ecuaci\u00f3n Diferencial Parcial<\/p>\n\n\n<span class=\"wp-katex-eq katex-display\" data-display=\"true\"> \\frac{\\partial ^2 u}{\\partial x^2} + \\frac{\\partial ^2 u}{\\partial y^2} = \\Big( x^2 + y^2 \\Big) e^{xy} <\/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 1<\/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\"> 0 \\lt y \\lt 0.5 <\/span>\n<\/div>\n<\/div>\n\n\n\n<p>Con las condiciones de frontera:<\/p>\n\n\n\n<p>u(0,y)=1, u(1,y)= y, 0\u2264y\u22640.5<br>u(x,0)=1, u(x,0.5)=x\/2, 0\u2264x\u22641<\/p>\n\n\n\n<p>Aproxime la soluci\u00f3n con tama\u00f1os de paso \u0394x = 0.25, \u0394y = 0.25<br>Utilice diferencias finitas centradas para las variables independientes x,y<\/p>\n\n\n\n<p>a. Plantee las ecuaciones para usar un m\u00e9todo num\u00e9rico en un nodo i,j<\/p>\n\n\n\n<p>b. Realice la gr\u00e1fica de malla,<\/p>\n\n\n\n<p>c. desarrolle y obtenga el modelo discreto para u(x<sub>i<\/sub>,t<sub>j<\/sub>)<\/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 adjunte los archivos del algoritmo y resultados.<\/p>\n\n\n\n<p><strong>R\u00fabrica<\/strong>: Aproximaci\u00f3n de las derivadas parciales (5 puntos), construcci\u00f3n de la malla (10), construcci\u00f3n del sistema lineal (15), resoluci\u00f3n del sistema (5 puntos).<\/p>\n\n\n\n<p><strong>Referencia<\/strong>: <a href=\"https:\/\/blog.espol.edu.ec\/algoritmos101\/mn-eval\/mn-2e15\/2eva2012ti_t3-edp-eliptica-placa-rectangular\/\" data-type=\"post\" data-id=\"854\">2Eva2012TI_T3 EDP el\u00edptica, placa rectangular<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>2da Evaluaci\u00f3n 2023-2024 PAO I. 29\/Agosto\/2023 Tema 3 (35 puntos) Aproxime la soluci\u00f3n de la Ecuaci\u00f3n Diferencial Parcial Con las condiciones de frontera: u(0,y)=1, u(1,y)= y, 0\u2264y\u22640.5u(x,0)=1, u(x,0.5)=x\/2, 0\u2264x\u22641 Aproxime la soluci\u00f3n con tama\u00f1os de paso \u0394x = 0.25, \u0394y = 0.25Utilice diferencias finitas centradas para las variables independientes x,y a. Plantee las ecuaciones para [&hellip;]<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"wp-custom-template-entrada-mn","format":"standard","meta":{"footnotes":""},"categories":[22],"tags":[57],"class_list":["post-9030","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\/9030","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=9030"}],"version-history":[{"count":3,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/9030\/revisions"}],"predecessor-version":[{"id":17529,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/9030\/revisions\/17529"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=9030"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=9030"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=9030"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}