{"id":62008,"date":"2018-03-09T22:49:55","date_gmt":"2018-03-09T22:49:55","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/soluciones-numericas-de-ecuaciones-en-derivadas-parciales-generadas-a-partir-de-esquemas-semi-impla%c2%adcitos-y-el-metodo-de-autofunciones-discreto\/"},"modified":"2018-03-09T22:49:55","modified_gmt":"2018-03-09T22:49:55","slug":"soluciones-numericas-de-ecuaciones-en-derivadas-parciales-generadas-a-partir-de-esquemas-semi-impla%c2%adcitos-y-el-metodo-de-autofunciones-discreto","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/resolucion-de-ecuaciones-diferenciales-en-derivadas-parciales\/soluciones-numericas-de-ecuaciones-en-derivadas-parciales-generadas-a-partir-de-esquemas-semi-impla%c2%adcitos-y-el-metodo-de-autofunciones-discreto\/","title":{"rendered":"Soluciones num\u00e9ricas de ecuaciones en derivadas parciales generadas a partir de esquemas semi-impl\u00edcitos y el m\u00e9todo de autofunciones discreto."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Rosa Aloy Miguel <\/strong><\/h2>\n<p>En esta tesis se desarrolla una t\u00e9cnica num\u00e9rica discreta, alternativa a las t\u00e9cnicas algebraicas habituales, que combina un m\u00e9todo de autofunciones discreto con un esquema en diferencias semi-impl\u00edcitos para resolver problemas mixtos de ecuaciones en derivadas parciales de tipo parab\u00f3lico, hiperb\u00f3lico y el\u00edptico. Esta nueva t\u00e9cnica mimetiza las ventajas del conocido m\u00e9todo de autofunciones continuo a la vez que elimina sus desventajas computacionales y, adem\u00e1s, construye una soluci\u00f3n num\u00e9rica  para el problema discretizado en forma anal\u00edtica cerrada que ofrece las siguientes ventajas: se puede aplicar a diferentes t\u00e9rminos fuente sin necesidad de recalcularla y evita la acumulaci\u00f3n de errores de redondeo ya que el valor de dicha soluci\u00f3n en un punto de la malla no utiliza los valores calculados en instantes temporales anteriores.  las etapas caracter\u00edsticas de la t\u00e9cnica num\u00e9rica presentada en esta memoria son, en primer lugar, la discretizaci\u00f3n del problema continuo mediante un esquema semi-impl\u00edcito y, a continuaci\u00f3n, la comprobaci\u00f3n que es consistente con la ecuaci\u00f3n en derivadas parciales. Luego se procede a la separaci\u00f3n de las variables discretizadas y, posteriormente, a la construcci\u00f3n de la soluci\u00f3n del problema como combinaci\u00f3n lineal finita de las funciones propias del problema de sturm-liouville discreto homog\u00e9neo subyacente en el problema continuo. Se finaliza con el estudio de la estabilidad de la soluci\u00f3n num\u00e9rica construida.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Soluciones num\u00e9ricas de ecuaciones en derivadas parciales generadas a partir de esquemas semi-impl\u00edcitos y el m\u00e9todo de autofunciones discreto.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Soluciones num\u00e9ricas de ecuaciones en derivadas parciales generadas a partir de esquemas semi-impl\u00edcitos y el m\u00e9todo de autofunciones discreto. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Rosa Aloy Miguel <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Polit\u00e9cnica de Valencia<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 17\/12\/2007<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li> J\u00f3dar S\u00e1nchez Lucas Antonio<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: rafael Bru Garc\u00eda <\/li>\n<li> Solis lozano Francisco Javier (vocal)<\/li>\n<li> Chen charpentier benito Miguel (vocal)<\/li>\n<li>Fernando Casas perez (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Rosa Aloy Miguel En esta tesis se desarrolla una t\u00e9cnica num\u00e9rica discreta, alternativa a las t\u00e9cnicas algebraicas [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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