{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 228 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 1 18 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 1 14 25 1 1 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 1 18 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 261 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 1 18 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 1 18 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 265 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 266 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 267 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 270 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 271 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 272 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 273 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 274 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 275 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 276 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 277 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 278 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 279 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 280 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 281 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 282 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 283 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 284 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 285 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 286 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 287 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 288 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 289 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 290 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 291 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 292 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 293 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 294 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 295 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 296 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 297 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 298 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 299 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 300 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE " Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 4 4 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE " " -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 299 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 300 41 "(4) Estimaci\363n del error y cambio de paso" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 0 "" } {TEXT 260 55 "Ejercicio 04-08 (del EXAMEN EXTRAORDINARIO de 14JUL04) " }}{PARA 4 "" 0 "" {TEXT -1 89 "\nPara un problema escalar se dise \361an tres m\351todos num\351ricos de integraci\363n de ecuaciones " }}{PARA 4 "" 0 "" {TEXT -1 69 "diferenciales que designaremos con los \+ nombres de M1 , M2 y M3 . " }}{PARA 4 "" 0 "" {TEXT -1 91 "Para de terminar cu\341l es el de orden m\341s alto, se realiza la integraci \363n de un problema test" }}{PARA 4 "" 0 "" {TEXT -1 91 "entre 0 y \+ 1 . Los dos primeros m\351todos son de paso fijo. Para ellos se emple an los pasos" }}{PARA 4 "" 0 "" {TEXT -1 5 " " }{XPPEDIT 18 0 "1/2 ^4" "6#*&\"\"\"F$*$\"\"#\"\"%!\"\"" }{TEXT -1 12 " = 0.0625 , " } {XPPEDIT 18 0 "1/2^5" "6#*&\"\"\"F$*$\"\"#\"\"&!\"\"" }{TEXT -1 12 " = 0.0313 , " }{XPPEDIT 18 0 "1/2^6" "6#*&\"\"\"F$*$\"\"#\"\"'!\"\"" } {TEXT -1 12 " = 0.0156 , " }{XPPEDIT 18 0 "1/2^7" "6#*&\"\"\"F$*$\"\"# \"\"(!\"\"" }{TEXT -1 11 " = 0.0078 ," }{TEXT 258 2 " " }{XPPEDIT 18 0 "1/2^8" "6#*&\"\"\"F$*$\"\"#\"\")!\"\"" }{TEXT -1 10 " = 0.0039 " }} {PARA 4 "" 0 "" {TEXT -1 46 "Los n\372meros de pasos son, en todos los casos, " }}{PARA 4 "" 0 "" {TEXT -1 28 " 16 , 32 , 64 , 128 , 256 " }}{PARA 4 "" 0 "" {TEXT -1 42 "Los n\372meros de evaluaciones son pa ra el M1" }}{PARA 4 "" 0 "" {TEXT -1 29 " 32 , 64 , 128 , 256 , 512 " }}{PARA 4 "" 0 "" {TEXT -1 12 "y para el M2" }}{PARA 4 "" 0 "" {TEXT -1 29 " 48 , 96 , 192 , 384 , 768" }}{PARA 4 "" 0 "" {TEXT -1 60 "El m\351todo M3 es un par encajado. Se prueba con tolerancias " }}{PARA 4 "" 0 "" {TEXT -1 37 " 0.001 , 0.0005 , 0.0001 , 0.00005 \+ " }}{PARA 4 "" 0 "" {TEXT -1 83 "y para ellas se han necesitado en el \+ c\341lculo los siguientes n\372meros de evaluaciones" }}{PARA 4 "" 0 " " {TEXT -1 26 " 128 , 220 , 336 , 448 " }}{PARA 4 "" 0 "" {TEXT -1 80 "Para cada m\351todo se calcula el log[10] del error cometido en l a aproximaci\363n de" }}{PARA 4 "" 0 "" {TEXT -1 79 "la soluci\363n en x=1 , error medido en m\363dulo. Los logaritmos de los errores que " }}{PARA 4 "" 0 "" {TEXT -1 29 "se obtienen son, para el M1 " }}{PARA 4 "" 0 "" {TEXT -1 59 " - 3.849 , - 4.701 , - 5.381 , - 6.014 , - 6.630 " }}{PARA 4 "" 0 "" {TEXT -1 12 " para el M2" }}{PARA 4 " " 0 "" {TEXT -1 57 " - 3.278 , - 4.861 , - 6.814 , - 7.743 , - \+ 8.659 " }}{PARA 4 "" 0 "" {TEXT -1 14 "y para el M3" }}{PARA 4 "" 0 "" {TEXT -1 58 " - 7.561 , - 8.014 , - 8.643 , - 8.959 \+ " }}{PARA 4 "" 0 "" {TEXT -1 76 "Con estos datos, se debe constr uir la 'gr\341fica de eficiencia' que mezcla los" }}{PARA 4 "" 0 "" {TEXT -1 74 "resultados de M1 , M2 y M3 exhibiendo 'n\372mero de \+ evaluaciones versus " }}{PARA 4 "" 0 "" {TEXT -1 77 "log[10] del error '. Adem\341s de dir\341 qu\351 m\351todo es m\341s interesante en cuan to al" }}{PARA 4 "" 0 "" {TEXT -1 30 "orden efectivo que se obtiene." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface(labeling=false):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Digits:=20:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 25 "with(linalg):with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have been red efined and unprotected\n" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the \+ name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 15 "Variables lista" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "lista1eval:=[32 , 64 , 128 , 256 , 512]:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "listalog1eval:=[0,0,0,0,0]: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "for i from 1 to 5 do li sta1logeval[i]:=log[10](lista1eval[i]): od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "lista1logerro:=[ -3.849, -4.701, -5.381, -6.014, - 6.630]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "lista2eval:=[48 \+ , 96 , 192 , 384 , 768]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "listalog2eval:=[0,0,0,0,0]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "for i from 1 to 5 do lista2logeval[i]:=log[10](lista2eval[i]): o d:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "lista2logerro:=[-3.27 8, -4.861, -6.814, -7.743, -8.659]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "lista3eval:=[128 , 220 , 336 , 448]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "listalog3eval:=[0,0,0,0]:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "for i from 1 to 4 do lista3l ogeval[i]:=log[10](lista3eval[i]): od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "lista3logerro:=[-7.561, -8.014, -8.643, -8.959]: " } }}{EXCHG {PARA 0 "" 0 "" {TEXT 256 69 "Gr\341ficas comparadas 'n\372me ro de evaluaciones versus log[10] del error'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "listagra1:=[seq([lista1eval[i],lista1logerro[i]] ,i=1..5)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "gra11:=plot(l istagra1,style=LINE):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "gr a12:=plot(listagra1,style=POINT,symbol=BOX):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "gra13:=textplot([400., -6.1,`M1`]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "listagra2:=[seq([lista2eval[i],list a2logerro[i]],i=1..5)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 " gra21:=plot(listagra2,style=LINE):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "gra22:=plot(listagra2,style=POINT,symbol=CIRCLE):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "gra23:=textplot([400., -7.5 ,`M2`]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "listagra3:=[seq ([lista3eval[i],lista3logerro[i]],i=1..4)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "gra31:=plot(listagra3,style=LINE):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "gra32:=plot(listagra3,style=POINT,s ymbol=DIAMOND):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "gra33:=t extplot([400, -8.5,`M3`]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "display(gra11,gra12,gra13,gra21,gra22,gra23,gra31,gra32,gra33);" } }{PARA 13 "" 1 "" {GLPLOT2D 496 496 496 {PLOTDATA 2 "6--%'CURVESG6%7'7 $$\"#K\"\"!$!%\\Q!\"$7$$\"#kF*$!%,ZF-7$$\"$G\"F*$!%\"Q&F-7$$\"$c#F*$!% 9gF-7$$\"$7&F*$!%ImF--%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*FI-%&STYLEG6#%%L INEG-F$6&F&FB-FK6#%&POINTG-%'SYMBOLG6#%$BOXG-%%TEXTG6$7$$\"$+%F*$!#hFH Q#M16\"-F$6%7'7$$\"#[F*$!%yKF-7$$\"#'*F*$!%h[F-7$$\"$#>F*$!%9oF-7$$\"$ %QF*$!%VxF-7$$\"$o(F*$!%f')F-FBFJ-F$6&F]oFBFP-FT6#%'CIRCLEG-FX6$7$Fen$ !#vFHQ#M2Fjn-F$6%7&7$F4$!%hvF-7$$\"$?#F*$!%9!)F-7$$\"$O$F*$!%V')F-7$$ \"$[%F*$!%f*)F-FBFJ-F$6&FdqFBFP-FT6#%(DIAMONDG-FX6$7$Fen$!#&)FHQ#M3Fjn -%+AXESLABELSG6%Q!FjnFes-%%FONTG6#%(DEFAULTG-%%VIEWG6$FisFis" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "C urve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" }} }}{EXCHG {PARA 0 "" 0 "" {TEXT 262 73 "Comparaci\363n 'log[10] del n \372mero de evaluaciones versus log[10] del error'" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 298 48 "Recordemos lo que ya sabemos de otros problemas: " }{TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 290 92 "Hay un tipo de gr\341 ficas que sirve para comprobar el orden 'efectivo' de los m\351todos, \+ o sea, " }}{PARA 4 "" 0 "" {TEXT 264 90 "el orden con que, en la pr \341ctica, parecen comportarse. En estas gr\341ficas se debe presentar " }}{PARA 4 "" 0 "" {TEXT 265 94 "en el eje de abscisas el log[10] del paso empleado y en el de ordenadas el log[10] del error. " }}{PARA 4 "" 0 "" {TEXT 266 90 "Entonces el aspecto de la gr\341fica se aproxima a una recta (o se puede aproximar utilizando" }}{PARA 4 "" 0 "" {TEXT 267 91 "la regresi\363n lineal). La pendiente de esa recta es el orden con que se comporta el m\351todo. " }}{PARA 4 "" 0 "" {TEXT 268 59 "En efecto, si el m\351todo es de orden p , el error ser\341 \+ O(" }{XPPEDIT 18 0 "h^p" "6#)%\"hG%\"pG" }{TEXT 269 37 ") . Considera ndo que, aproximadamente" }}{PARA 4 "" 0 "" {TEXT 270 20 "se tiene E (h) = K " }{XPPEDIT 18 0 "h^p" "6#)%\"hG%\"pG" }{TEXT 271 78 " , resu lta que el cociente incremental (la pendiente aproximada de la recta) \+ " }}{PARA 4 "" 0 "" {TEXT 272 43 "entre dos puntos correspondientes a \+ pasos " }{XPPEDIT 18 0 "h[1]" "6#&%\"hG6#\"\"\"" }{TEXT 273 3 " < " } {XPPEDIT 18 0 "h[2]" "6#&%\"hG6#\"\"#" }{TEXT 274 5 " es " }}{PARA 4 "" 0 "" {TEXT 275 5 " " }{XPPEDIT 18 0 "(log[10] (E(h[2))-log[10] \+ (E(h[1])))/(log[10] (h[2])-log[10] (h[1]))" "6#*&,&-&%$logG6#\"#56#-% \"EG6#&%\"hG6#\"\"#\"\"\"-&F'6#F)6#-F,6#&F/6#F2!\"\"F2,&-&F'6#F)6#&F/6 #F1F2-&F'6#F)6#&F/6#F2F;F;" }{TEXT -1 4 " = " }{XPPEDIT 18 0 "(log[10 ] (K)+p*log[10](h[2])-log[10] (K)-p*log[10](h[1]))/(log[10] (h[2])-log [10] (h[1]))" "6#*&,*-&%$logG6#\"#56#%\"KG\"\"\"*&%\"pGF,-&F'6#F)6#&% \"hG6#\"\"#F,F,-&F'6#F)6#F+!\"\"*&F.F,-&F'6#F)6#&F46#F,F,F;F,,&-&F'6#F )6#&F46#F6F,-&F'6#F)6#&F46#F,F;F;" }{TEXT -1 24 " = p \+ " }}{PARA 4 "" 0 "" {TEXT 276 89 "Esta pendiente se puede estudiar \+ cuando se utilizan los segmentos correspondientes a los " }}{PARA 4 " " 0 "" {TEXT 280 69 "menores valores de h , los mas representativos d el efecto del orden." }}{PARA 4 "" 0 "" {TEXT 277 101 "Algo semejante \+ ocurre cuando se presenta en el eje de abscisas el log[10] del numero de evaluaciones" }}{PARA 4 "" 0 "" {TEXT 281 97 "y en el de ordenadas el log[10] del error. Entonces tambi\351n el aspecto de la gr\341fica se aproxima " }}{PARA 4 "" 0 "" {TEXT 295 98 "a una recta (o se puede aproximar utilizando la regresi\363n lineal). Pero la pendiente de es a recta " }}{PARA 4 "" 0 "" {TEXT 296 91 "es ahora igual a menos el or den con que se comporta el m\351todo, debido a que en el cociente " }} {PARA 4 "" 0 "" {TEXT 297 39 "antes expuesto el denominador es ahora \+ " }}{PARA 4 "" 0 "" {TEXT 284 5 " " }{XPPEDIT 18 0 "log[10] (eval( h[2]))-log[10] (eval(h[1]))" "6#,&-&%$logG6#\"#56#-%%evalG6#&%\"hG6#\" \"#\"\"\"-&F&6#F(6#-F+6#&F.6#F1!\"\"" }{TEXT 282 3 " = " }{XPPEDIT 18 0 "log[10] (m/h[2])-log[10] (m/h[1])" "6#,&-&%$logG6#\"#56#*&%\"mG\"\" \"&%\"hG6#\"\"#!\"\"F,-&F&6#F(6#*&F+F,&F.6#F,F1F1" }{TEXT 283 4 " = \+ " }}{PARA 4 "" 0 "" {TEXT 285 12 " = " }{XPPEDIT 18 0 "log[10 ](m)-log[10] (h[2])-log[10](m)+log[10] (h[1])" "6#,*-&%$logG6#\"#56#% \"mG\"\"\"-&F&6#F(6#&%\"hG6#\"\"#!\"\"-&F&6#F(6#F*F4-&F&6#F(6#&F16#F+F +" }{TEXT 286 4 " = " }{XPPEDIT 18 0 "log[10] (h[1])-log[10] (h[2])" "6#,&-&%$logG6#\"#56#&%\"hG6#\"\"\"F--&F&6#F(6#&F+6#\"\"#!\"\"" } {TEXT 287 21 " " }}{PARA 4 "" 0 "" {TEXT 278 87 "e n el supuesto de que m es el n\372mero de evaluaciones por paso del \+ m\351todo en cuesti\363n." }}{PARA 4 "" 0 "" {TEXT 279 101 "Esta idea \+ se emplea especialmente cuando el m\351todo es de paso variable y se d esea averiguar su orden " }}{PARA 4 "" 0 "" {TEXT 288 104 "efectivo, y a que, entonces, no tiene sentido hablar del paso del m\351todo, pero \+ s\355 que lo tiene hablar de " }}{PARA 4 "" 0 "" {TEXT 289 42 "las eva luaciones realizadas por el mismo. " }}{PARA 4 "" 0 "" {TEXT 291 95 "Y esto es justamente lo que sucede en este caso en el que hay que compa rar con m\351todos de paso " }}{PARA 4 "" 0 "" {TEXT 292 97 "variable; por ello no emplearemos las gr\341ficas 'log[10] del paso versus log[ 10] del error' , que " }}{PARA 4 "" 0 "" {TEXT 293 106 "carecen ahora \+ de sentido, sino las gr\341ficas 'log[10] del n\372mero de evaluacione s versus log[10] del error'," }}{PARA 4 "" 0 "" {TEXT 294 70 "que son \+ las que ahora pueden servir para detectar el 'orden efectivo'." }}} {EXCHG {PARA 0 "" 0 "" {TEXT 263 77 "Orden efectivo de los m\351todos, empleando la pendiente del \372ltimo segmento. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "pendm1:=evalf((lista1logerro[5]-lista1loger ro[4])/(lista1logeval[5]-lista1logeval[4]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'pendm1G$!5d?:1X1xIY?!#>" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 87 "pendm2:=evalf((lista2logerro[5]-lista2logerro[4])/( lista2logeval[5]-lista2logeval[4]));" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%'pendm2G$!53\"R#o\"\\8')G/$!#>" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "pendm3:=evalf((lista3logerro[4]-lista3logerro[3])/(li sta3logeval[4]-lista3logeval[3]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%'pendm3G$!5-cX(p$)fR#HD!#>" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 50 " M\351todo m\341s interesante en cuanto al orden efectivo" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 261 66 "El m\351todo M2 p resenta el mejor orden efectivo de los tres m\351todos." }{TEXT -1 0 " " }}}}{MARK "0 3 1" 15 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }