{"id":10621,"date":"2025-01-29T06:25:30","date_gmt":"2025-01-29T11:25:30","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/analisisnumerico\/?p=10621"},"modified":"2025-12-13T07:27:44","modified_gmt":"2025-12-13T12:27:44","slug":"2eva2024paoii_t3-edp-eliptica-con-funcion-en-borde-superior","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/mn-evalua\/mn-2e25\/2eva2024paoii_t3-edp-eliptica-con-funcion-en-borde-superior\/","title":{"rendered":"2Eva2024PAOII_T3 EDP El\u00edptica con funci\u00f3n en borde superior"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">2da Evaluaci\u00f3n 2024-2025 PAO II. 28\/Enero\/2025<\/h2>\n\n\n\n<p><strong>Tema 3<\/strong>. (35 puntos) Considere la ecuaci\u00f3n diferencial parcial, tipo el\u00edptica descrita sobre una placa en el plano x,y:<\/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} <\/span>\n\n\n\n<p class=\"has-text-align-center\">0\u2264x\u22641 ; 0\u2264y\u22641.5<\/p>\n\n\n\n<p>Con condiciones en frontera en los intervalos definidos para una placa.<\/p>\n\n\n\n<figure class=\"wp-block-image alignright size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"415\" height=\"413\" src=\"http:\/\/blog.espol.edu.ec\/algoritmos101\/files\/2025\/01\/ElpiticaImplicitoT3.png\" alt=\"El\u00edptica Impl\u00edcito T3\" class=\"wp-image-17560\" \/><\/figure>\n\n\n\n<p>u(0, y) = 0 ; u(1, y) = 0<\/p>\n\n\n\n<p>u(x, 0) = 0<\/p>\n\n\n\n<p>u(x, 1.5) = 100 sin(\u03c0x)<\/p>\n\n\n\n<p>Utilice diferencias finitas para las variables independientes x,y<\/p>\n\n\n\n<p>a. Plantee las ecuaciones discretas a usar un m\u00e9todo num\u00e9rico en un nodo i,j<\/p>\n\n\n\n<p>b. Realice la gr\u00e1fica de malla, detalle los valores de i, j, x<sub>i<\/sub>, y<sub>j<\/sub><\/p>\n\n\n\n<p>c. Desarrolle y obtenga el modelo discreto para u(x<sub>i<\/sub>,y<sub>j<\/sub>)<\/p>\n\n\n\n<p>d. Determine el valor de Lambda \u03bb, considerando \u0394x = 1\/4 , \u0394y = 1\/8<\/p>\n\n\n\n<p>e. Desarrolle la ecuaci\u00f3n para al menos tres nodos i,j diferentes y consecutivos.<\/p>\n\n\n\n<p>f. (<strong><em>Extra<\/em><\/strong>) Estime el error de u(x<sub>i<\/sub>,t<sub>j<\/sub>) y adjunte los archivos del algoritmo.py, resultados.txt, gr\u00e1ficas.png<\/p>\n\n\n\n<p><strong>R\u00fabrica<\/strong>: Selecci\u00f3n de diferencias finitas divididas (5 puntos), literal b (5 puntos), literal c (5 puntos), literal d (5 puntos), literal e (15 puntos). literal f extra (5 puntos)<\/p>\n\n\n\n<p><strong>Referencia<\/strong>: Chapter 13: Partial Differential Equations (Part 2 - Elliptic PDEs). Lindsey Westover. 18 Marzo 2021. https:\/\/youtu.be\/0eI5zrhtEjE?si=a8rQhpEEirvMBC26&amp;t=633<\/p>\n","protected":false},"excerpt":{"rendered":"<p>2da Evaluaci\u00f3n 2024-2025 PAO II. 28\/Enero\/2025 Tema 3. (35 puntos) Considere la ecuaci\u00f3n diferencial parcial, tipo el\u00edptica descrita sobre una placa en el plano x,y: 0\u2264x\u22641 ; 0\u2264y\u22641.5 Con condiciones en frontera en los intervalos definidos para una placa. u(0, y) = 0 ; u(1, y) = 0 u(x, 0) = 0 u(x, 1.5) = [&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-10621","post","type-post","status-publish","format-standard","hentry","category-mn-2e25","tag-edp"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/10621","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=10621"}],"version-history":[{"count":2,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/10621\/revisions"}],"predecessor-version":[{"id":17561,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/10621\/revisions\/17561"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=10621"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=10621"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=10621"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}