{"id":4725,"date":"2020-01-29T09:55:21","date_gmt":"2020-01-29T14:55:21","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1013\/?p=4725"},"modified":"2025-12-13T04:02:38","modified_gmt":"2025-12-13T09:02:38","slug":"2eva2019tii_t3-edp-eliptica-placa-en-11","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/mn-2eva20\/2eva2019tii_t3-edp-eliptica-placa-en-11\/","title":{"rendered":"2Eva2019TII_T3 EDP el\u00edptica, placa en (1,1)"},"content":{"rendered":"\n

2da Evaluaci\u00f3n II T\u00e9rmino 2019-2020. 28\/Enero\/2020. MATG1013<\/h2>\n\n\n\n

Tema 3<\/strong>. (30 Puntos) Para la ecuaci\u00f3n diferencial parcial el\u00edptica mostrada:<\/p>\n\n\n \\frac{\\partial ^2 u}{\\partial x^2} + \\frac{\\partial ^2 u}{\\partial y^2} = \\frac{x}{y} + \\frac{y}{x} <\/span>\n\n\n\n

\n
\n

1 <\u00a0 x <\u00a02<\/p>\n<\/div>\n\n\n\n

\n

1 <\u00a0 y <\u00a02<\/p>\n<\/div>\n<\/div>\n\n\n\n

Y con las siguientes condiciones de frontera:<\/p>\n\n\n\n

\n
u(x,1)= x \\ln (x)<\/span>\n\n\nu(x,2) = x \\ln (4x^{2})<\/span>\n\n\n1 < x < 2 <\/span>\n<\/div>\n\n\n\n
u(1,y)= y \\ln(y)<\/span>\n\n\n u(2,y) = 2y \\ln (2y) <\/span>\n\n\n 1 < y < 2 <\/span>\n<\/div>\n<\/div>\n\n\n\n

Considere los valores hx=hy=0.25<\/p>\n\n\n\n

Realice la aproximaci\u00f3n num\u00e9rica para la soluci\u00f3n.<\/p>\n\n\n\n

Para resolver el sistema de ecuaciones utilice el m\u00e9todo de Gauss-Seidel para dos iteraciones.<\/p>\n\n\n\n

R\u00fabrica<\/strong>: Plantear la malla (5 puntos), calcular los bordes (3 puntos), plantear las segundas derivadas (7 puntos), plantear las ecuaciones  (10 puntos), aproximar la soluci\u00f3n  (5 puntos)<\/p>\n","protected":false},"excerpt":{"rendered":"

2da Evaluaci\u00f3n II T\u00e9rmino 2019-2020. 28\/Enero\/2020. MATG1013 Tema 3. (30 Puntos) Para la ecuaci\u00f3n diferencial parcial el\u00edptica mostrada: 1 <\u00a0 x <\u00a02 1 <\u00a0 y <\u00a02 Y con las siguientes condiciones de frontera: Considere los valores hx=hy=0.25 Realice la aproximaci\u00f3n num\u00e9rica para la soluci\u00f3n. Para resolver el sistema de ecuaciones utilice el m\u00e9todo de Gauss-Seidel […]<\/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-4725","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\/4725","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=4725"}],"version-history":[{"count":5,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/4725\/revisions"}],"predecessor-version":[{"id":17471,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/4725\/revisions\/17471"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=4725"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=4725"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=4725"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}