{"id":955,"date":"2017-12-17T08:02:00","date_gmt":"2017-12-17T13:02:00","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1013\/?p=955"},"modified":"2025-12-13T03:20:34","modified_gmt":"2025-12-13T08:20:34","slug":"2eva2017ti_t3-edp-parabolica","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/mn-2eva20\/2eva2017ti_t3-edp-parabolica\/","title":{"rendered":"2Eva2017TI_T3 EDP parab\u00f3lica"},"content":{"rendered":"\n

2da Evaluaci\u00f3n I T\u00e9rmino 2017-2018. 28\/Agosto\/2017. MATG1013<\/h2>\n\n\n\n

Tema 3<\/strong>. (30 puntos) Use el m\u00e9todo de diferencias progresivas para aproximar la soluci\u00f3n de la siguiente ecuaci\u00f3n diferencial parcial parab\u00f3lica:<\/p>\n\n\n \\frac{\\partial u}{\\partial t} - \\frac{1}{\\pi ^2} \\frac{\\partial ^2 u}{\\partial x^2} =0 <\/span>\n\n\n\n

0 \u2264 x \u2264 1, t>0<\/p>\n\n\n\n

\n
\n

condiciones de borde:<\/p>\n\n\n\n

u(0,t) = u(1,t) = 0<\/p>\n\n\n\n

t>0<\/p>\n<\/div>\n\n\n\n

\n

condiciones iniciales:<\/p>\n\n\n\n

u(x,0) = cos(\u03c0(x-0.5))<\/p>\n\n\n\n

0 \u2264 x \u2264 1<\/p>\n<\/div>\n<\/div>\n\n\n\n

a) Use dx = 0.2 y dt = 0.01. Realice 3 pasos en el tiempo.<\/p>\n\n\n\n

b) Estime el error.<\/p>\n\n\n\n

c) Calcule la temperatura promedio para t=0 como el \u00e1rea bajo la curva, mediante el m\u00e9todo de Simpson. Repita para t=0.01 y calcule el porcentaje que disminuye.<\/p>\n\n\n\n

R\u00fabrica<\/strong>: Construir la malla hasta 5 puntos, plantear la ecuaci\u00f3n en el nodo i,j hasta 5 puntos, calcular el estimado de u(i,j) hasta la tercera fila hasta 5 puntos, calcular la temperatura media estimada hasta 5 puntos.<\/p>\n","protected":false},"excerpt":{"rendered":"

2da Evaluaci\u00f3n I T\u00e9rmino 2017-2018. 28\/Agosto\/2017. MATG1013 Tema 3. (30 puntos) Use el m\u00e9todo de diferencias progresivas para aproximar la soluci\u00f3n de la siguiente ecuaci\u00f3n diferencial parcial parab\u00f3lica: 0 \u2264 x \u2264 1, t>0 condiciones de borde: u(0,t) = u(1,t) = 0 t>0 condiciones iniciales: u(x,0) = cos(\u03c0(x-0.5)) 0 \u2264 x \u2264 1 a) Use […]<\/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-955","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\/955","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=955"}],"version-history":[{"count":7,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/955\/revisions"}],"predecessor-version":[{"id":17422,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/955\/revisions\/17422"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=955"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=955"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}