{"id":5837,"date":"2024-11-22T11:04:32","date_gmt":"2024-11-22T17:04:32","guid":{"rendered":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/?page_id=5837"},"modified":"2024-11-22T11:04:32","modified_gmt":"2024-11-22T17:04:32","slug":"mn6c","status":"publish","type":"page","link":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/unidad-6\/mn6c\/","title":{"rendered":"mn6c Euler"},"content":{"rendered":"\n

El m\u00e9todo de Euler es un m\u00e9todo de primer orden, lo que significa que el error local es proporcional al cuadrado del tama\u00f1o del paso, y el error global es proporcional al tama\u00f1o del paso<\/strong>.<\/p>\n\n\n\n

En su forma simple emplea la f\u00f3rmula<\/p>\n\n\n\n

y1 <\/sub>=  y0<\/sub> +  h*y\u00b4 <\/p>\n\n\n\n

donde h es el tama\u00f1o de paso, y0 es la condici\u00f3n inicial, y’ es la ecuaci\u00f3n diferencial. Para evaluar la estimaci\u00f3n siguiente o paso, se utiliza el valor inicial de x y se calcula el siguiente valor x + dx, se utiliza el valor calculado de y en el paso anterior.<\/p>\n\n\n\n

Ejemplo 1. <\/h3>\n\n\n\n

Resuelva la siguiente ecuaci\u00f3n diferencial por m\u00e9todo de Euler simple<\/p>\n\n\n\n

y\u2019 = (x + y \u2013 1)2  <\/sup>         y(0) = 2      h = 0.1<\/p>\n\n\n\n

Soluci\u00f3n.<\/p>\n\n\n\n

n = 0      h = 0.1        x0 <\/sub>= 0         y0<\/sub> = 2<\/p>\n\n\n\n

y1 <\/sub>=  y0<\/sub> +  h*y\u00b4 = 2 + 0.1 (0 + 2 \u2013 1)2<\/sup><\/p>\n\n\n\n

= 2 + 0.1 (1)2<\/sup><\/p>\n\n\n\n

= 2.1<\/p>\n\n\n\n

n = 1      h = 0.1        x1<\/sub> = 0 + 0.1 = 0.1          y1<\/sub> = 2.1<\/p>\n\n\n\n

y2<\/sub>= 2.1 + 0.1 (0.1 + 2.1 \u2013 1)2<\/sup><\/p>\n\n\n\n

y2<\/sub>= 2 + 0.1 (1.2)2<\/sup><\/p>\n\n\n\n

y2<\/sub>= 2.244<\/p>\n\n\n\n

n = 2      h = 0.1        x2<\/sub> = 0.2          y2<\/sub> = 2.244<\/p>\n\n\n\n

y3<\/sub>= 2.244 + 0.1 (0.2 + 2.244 \u2013 1)2<\/sup><\/p>\n\n\n\n

y3<\/sub>= 2.244 + 0.1 (1.444)2<\/sup><\/p>\n\n\n\n

y3<\/sub>= 2.4525136<\/p>\n\n\n\n

n = 3      h = 0.1        x3<\/sub> = 0.3          y3<\/sub> = 2.4525136<\/p>\n\n\n\n

= 2.4525136 + 0.1 (0.3 + 2.4525136 \u2013 1)2<\/sup><\/p>\n\n\n\n

= 2.4525136 + 0.1 (1.2)2<\/sup><\/p>\n\n\n\n

= 2.759644<\/p>\n\n\n\n

n = 4      h = 0.1        x4<\/sub> = 0.4          y4<\/sub> = 2.759644<\/p>\n\n\n\n

= 2.759644 + 0.1 (0.4 + 2.759644 \u2013 1)2<\/sup> = 2.759644 + 0.4664<\/p>\n\n\n\n

= 3.22605<\/p>\n\n\n\n

\n
\n
x<\/td>dy\/dx<\/td><\/tr>
0<\/td>2<\/td><\/tr>
0.1<\/td>2.1<\/td><\/tr>
0.2<\/td>2.244<\/td><\/tr>
0.3<\/td>2.4525<\/td><\/tr>
0.4<\/td>2.7596<\/td><\/tr>
0.5<\/td>3.226<\/td><\/tr>
0.6<\/td>3.969<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n\n
\n

<\/p>\n<\/div>\n<\/div>\n\n\n\n

\"\"<\/p>\n\n\n\n

\n
regresar<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

El m\u00e9todo de Euler es un m\u00e9todo de primer orden, lo que significa que el error local es proporcional al cuadrado del tama\u00f1o del paso, y el error global es proporcional al tama\u00f1o del paso. En su forma simple emplea la f\u00f3rmula y1 =  y0 +  h*y\u00b4 donde h es el tama\u00f1o de paso, y0 es la … Contin\u00faa leyendo mn6c Euler<\/span><\/a><\/p>\n","protected":false},"author":123458,"featured_media":0,"parent":3189,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0},"_links":{"self":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/5837"}],"collection":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/users\/123458"}],"replies":[{"embeddable":true,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/comments?post=5837"}],"version-history":[{"count":3,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/5837\/revisions"}],"predecessor-version":[{"id":6016,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/5837\/revisions\/6016"}],"up":[{"embeddable":true,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/3189"}],"wp:attachment":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/media?parent=5837"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}