{"id":1014,"date":"2017-08-10T09:30:58","date_gmt":"2017-08-10T14:30:58","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/matg1013\/?p=1014"},"modified":"2026-01-16T14:45:06","modified_gmt":"2026-01-16T19:45:06","slug":"diferenciacion-numerica-tablas","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/mn-u05\/diferenciacion-numerica-tablas\/","title":{"rendered":"5.7.2 Diferenciaci\u00f3n num\u00e9rica - Tablas con diferencias divididas"},"content":{"rendered":"\n
\n\n\n\n
\n

Diferencias Divididas<\/p>\n\n\n\n

hacia adelante<\/a><\/p>\n\n\n\n

centradas<\/a><\/p>\n\n\n\n

hacia atr\u00e1s<\/a><\/p>\n<\/div>\n\n\n\n

\n\n\n\n

Referencia<\/strong>: Chapra Fig.23.1 p669, Burden 4.1 p167, Rodr\u00edguez 8.2,3,4,6 p324<\/p>\n\n\n\n

Diferencias divididas hacia adelante<\/h2>\n\n\n\n

Primera derivada<\/p>\n\n\n f'(x_i) = \\frac{f(x_{i+1})-f(x_i)}{h} + O(h) <\/span>\n\n\n f'(x_i) = \\frac{-f(x_{i+2})+4f(x_{i+1})-3f(x_i)}{2h} + O(h^2)<\/span>\n\n\n\n

Segunda derivada<\/p>\n\n\n f''(x_i) = \\frac{f(x_{i+2})-2f(x_{i+1})+f(x_i)}{h^2} + O(h) <\/span>\n\n\n f''(x_i) = \\frac{-f(x_{i+3})+4f(x_{i+2})-5f(x_{i+1})+2f(x_i)}{h^2}<\/span>\n\n\n + O(h^2)<\/span>\n\n\n\n

Tercera derivada<\/p>\n\n\n f'''(x_i) = \\frac{f(x_{i+3})-3f(x_{i+2})+3f(x_{i+1})-f(x_i)}{h^3}<\/span>\n\n\n + O(h)<\/span>\n\n\n f'''(x_i) = \\frac{-3f(x_{i+4})+14f(x_{i+3})-24f(x_{i+2})+18f(x_{i+1})-5f(x_i)}{2h^3} <\/span>\n\n\n + O(h^2) <\/span>\n\n\n\n

Cuarta derivada<\/p>\n\n\n f''''(x_i) = \\frac{f(x_{i+4})-4f(x_{i+3})+6f(x_{i+2})-4f(x_{i+1})+f(x_i)}{h^3}<\/span>\n\n\n + O(h) <\/span>\n\n\n\n

\n\n\n\n
\n

Diferencias Divididas<\/p>\n\n\n\n

hacia adelante<\/a><\/p>\n\n\n\n

centradas<\/a><\/p>\n\n\n\n

hacia atr\u00e1s<\/a><\/p>\n<\/div>\n\n\n\n

\n\n\n\n

Diferencias divididas centradas<\/h2>\n\n\n\n

Primera derivada<\/p>\n\n\n f'(x_i) = \\frac{f(x_{i+1})-f(x_{i-1})}{2h} + O(h^2) <\/span>\n\n\n f'(x_i) = \\frac{-f(x_{i+2})+8f(x_{i+1})-8f(x_{i-1}) +f(x_{i-2})}{12h}<\/span>\n\n\n + O(h^4)<\/span>\n\n\n\n

Segunda derivada<\/p>\n\n\n f''(x_i) = \\frac{f(x_{i+1})-2f(x_{i})+f(x_{i-1})}{h^2} + O(h^2) <\/span>\n\n\n f''(x_i) = \\frac{-f(x_{i+2})+16f(x_{i+1})-30f(x_{i})+16f(x_{i-1})-f(x_{i-2})}{12h^2} <\/span>\n\n\n + O(h^4)<\/span>\n\n\n\n

Tercera derivada<\/p>\n\n\n f'''(x_i) = \\frac{f(x_{i+2})-2f(x_{i+1})+2f(x_{i-1})-f(x_{i-2})}{2h^3}<\/span>\n\n\n + O(h^2) <\/span>\n\n\n f'''(x_i) = \\frac{-f(x_{i+3})+8f(x_{i+2})-13f(x_{i+1})+13f(x_{i-1})-8f(x_{i-2})+f(x_{i-3})}{8h^3}<\/span>\n\n\n + O(h^4)<\/span>\n\n\n\n

\n\n\n\n
\n

Diferencias Divididas<\/p>\n\n\n\n

hacia adelante<\/a><\/p>\n\n\n\n

centradas<\/a><\/p>\n\n\n\n

hacia atr\u00e1s<\/a><\/p>\n<\/div>\n\n\n\n

\n\n\n\n

Diferencias divididas hacia atr\u00e1s<\/h2>\n\n\n\n

Primera derivada<\/p>\n\n\n f'(x_i) = \\frac{f(x_{i})-f(x_{i-1})}{h} + O(h) <\/span>\n\n\n f'(x_i) = \\frac{3f(x_{i})-4f(x_{i-1})+f(x_{i-2})}{2h}<\/span>\n\n\n + O(h^2)<\/span>\n\n\n\n

Segunda derivada<\/p>\n\n\n f''(x_i) = \\frac{f(x_{i})-2f(x_{i-1})+f(x_{i-2})}{h^2} + O(h)<\/span>\n\n\n f''(x_i) = \\frac{2f(x_{i})-5f(x_{i-1})+4f(x_{i-2})-f(x_{i-3})}{h^2}<\/span>\n\n\n + O(h^2)<\/span>\n\n\n\n

Tercera derivada<\/p>\n\n\n f'''(x_i) = \\frac{f(x_{i})-3f(x_{i-1})+3f(x_{i-2})-f(x_{i-3})}{h^3} + O(h) <\/span>\n\n\n f'''(x_i) = \\frac{5f(x_{i})-18f(x_{i-1})+24f(x_{i-2})-14f(x_{i-3})+3f(x_{i-4})}{2h^3} <\/span>\n\n\n + O(h^2)<\/span>\n\n\n\n

\n\n\n\n
\n

Diferencias Divididas<\/p>\n\n\n\n

hacia adelante<\/a><\/p>\n\n\n\n

centradas<\/a><\/p>\n\n\n\n

hacia atr\u00e1s<\/a><\/p>\n<\/div>\n\n\n\n

\n","protected":false},"excerpt":{"rendered":"

Diferencias Divididas hacia adelante centradas hacia atr\u00e1s Referencia: Chapra Fig.23.1 p669, Burden 4.1 p167, Rodr\u00edguez 8.2,3,4,6 p324 Diferencias divididas hacia adelante Primera derivada Segunda derivada Tercera derivada Cuarta derivada Diferencias Divididas hacia adelante centradas hacia atr\u00e1s Diferencias divididas centradas Primera derivada Segunda derivada Tercera derivada Diferencias Divididas hacia adelante centradas hacia atr\u00e1s Diferencias divididas hacia […]<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"wp-custom-template-entrada-mn-unidades","format":"standard","meta":{"footnotes":""},"categories":[39],"tags":[],"class_list":["post-1014","post","type-post","status-publish","format-standard","hentry","category-mn-u05"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1014","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=1014"}],"version-history":[{"count":2,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1014\/revisions"}],"predecessor-version":[{"id":13675,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/1014\/revisions\/13675"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=1014"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=1014"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=1014"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}