{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 "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 }{CSTYLE "" -1 259 "" 1 18 0 0 0 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 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 263 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 265 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 266 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 267 "" 1 14 25 1 1 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 268 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 270 "" 1 18 0 0 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}}{PARA 0 "" 0 "" {MPLTEXT 0 21 42 "# lineal de ecuacion 'stiff', el problema \+ " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 27 "# y'= - 110 y , y(0) = 1" }} {PARA 0 "" 0 "" {MPLTEXT 0 21 20 "# de soluci\363n exacta" }}{PARA 0 " " 0 "" {MPLTEXT 0 21 9 "# y(x) = " }{XPPEDIT 18 0 "e^(-110*x);" "6#)% \"eG,$*&\"$5\"\"\"\"%\"xGF(!\"\"" }{MPLTEXT 0 21 12 " " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 0 21 43 "# que integramos en \+ [0,1] con diferentes " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 21 "# valores \+ del paso h" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface(labeling=false):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Digits:=10:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 261 25 "EULER explicito (e. aut.)" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 156 "Euler:=proc(f::procedure,yt otalini::list,nit::posint,h::numeric)\nlocal x0,y0,k,k1:\ny0:=ytotalin i[2]:\nfor k from 1 to nit do\nk1:=f(y0):\ny0:=y0+h*k1:\nod:\nend:" }} }{EXCHG {PARA 0 "" 0 "" {TEXT 262 25 "EULER implicito (e. aut.)" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 186 "EulerI mplicito:=proc(f::procedure,ytotalini::list,nit::posint,h::numeric)\nl ocal x0,y0,k,k1e,k1:\ny0:=ytotalini[2]:\nfor k from 1 to nit do\nk1:=s olve(k1e=f(y0+h*k1e)):\ny0:=y0+h*k1:\nod:\nend:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 270 39 "EULER implicito aproximado (e. no aut.)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 219 "EulerImplicitoA proximado:=proc(f::procedure,ytotalini::list,nit::posint,h::numeric)\n local x0,y0,k,k1,k10,kt1:\ny0:=ytotalini[2]:\nfor k from 1 to nit do\n kt1:=f(y0):\nk10:=f(y0+h*kt1):\nk1:=f(y0+h*k10):\ny0:=y0+h*k1:\nod:\ne nd:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 263 9 "Caso 1 : " }}{PARA 4 "" 0 "" {TEXT -1 88 "El problema escalar y' = - 110 y , y(0) = 1 , del q ue se conoce la verdadera soluci\363n" }}{PARA 4 "" 0 "" {TEXT -1 7 " \+ " }{XPPEDIT 18 0 "y(x) = exp(-110*x);" "6#/-%\"yG6#%\"xG-%$expG6 #,$*&\"$5\"\"\"\"F'F.!\"\"" }}{PARA 4 "" 0 "" {TEXT 267 109 "se integr a num\351ricamente en el intervalo [ 0 , 1 ] con EULER , EULER impli cito y EULER impl\355cito aproximado" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 268 41 "La ecuaci\363n (aut.) y la condicion inicial" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "f:=unapply(-110*y,y);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"fGf*6#%\"yG6\"6$%)operatorG%&arrowGF(,$*&\"$5\"\" \"\"9$F/!\"\"F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 15 "Solucion \+ exacta" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "ecu2:=diff(y(x),x )=f(y(x));ini:=y(0)=1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ecu2G/-%% diffG6$-%\"yG6#%\"xGF,,$*&\"$5\"\"\"\"F)F0!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$iniG/-%\"yG6#\"\"!\"\"\"" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 30 "solucion2:=dsolve(\{ecu2,ini\});" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%*solucion2G/-%\"yG6#%\"xG-%$expG6#,$*&\"$5\"\"\"\"F )F0!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "u2:=unapply(sub s(solucion2,y(x)),x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "gr a2:=plot(u2,0..1.):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 5 "Pasos" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "pasos2: =[20,50,200,20,20,50,200];h2:=[seq(1./pasos2[i],i=1..7)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'pasos2G7)\"#?\"#]\"$+#F&F&F'F(" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%#h2G7)$\"+++++]!#6$\"+++++?F($F'!#7F&F&F)F+" } }}{EXCHG {PARA 0 "" 0 "" {TEXT 264 44 "Caso 2a : EULER con paso 'grand e' (20 pasos)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "ytotalini2 :=[0.,1.]:x1:=ytotalini2[1]:y1:=ytotalini2[2]:x12a[0]:=x1:y12a[0]:=y1: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "for i from 1 to pasos 2[1] do y1:=Euler(f,ytotalini2,1,h2[1]):x1:=x1+h2[1]:x12a[i]:=x1:y12a[ i]:=y1: ytotalini2:=[x1,y1]: od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "datos2a:=[seq([x12a[i],y12a[i]],i=0..pasos2[1])]:" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 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=x1:y12b[0]:=y1: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "for i from 1 to pasos2[2] do y1:=Euler(f,ytotalini2,1,h2[2]):x1:=x1+h2[2]:x 12b[i]:=x1:y12b[i]:=y1: ytotalini2:=[x1,y1]: od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "datos2b:=[seq([x12b[i],y12b[i]],i=0..pasos2[2 ])]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "gra2b:=listplot(dat os2b):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "display(gra2,gra2 b,view=[0..0.2, -.1...1.1]);" }{TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT2D 424 424 424 {PLOTDATA 2 "6&-%'CURVESG6$7ao7$$\"\"!F)$\"\"\"F )7$$\"3/LL3x1h6o!#@$\"3)f.\">%[0\"y#*!#=7$$\"3immTN@Ki8!#?$\"3(4exv8C$ 3')F27$$\"3#***\\7.K[V?F6$\"37l_0RR*o)zF27$$\"3ALL$3FWYs#F6$\"3J!3gdWC .T(F27$$\"3_m;aQ`!eS$F6$\"3w]T)z=x`(oF27$$\"3%)***\\iSmp3%F6$\"3)*p$\"3S?b+3vU:IF 27$$\"3gmmTN@Ki8Fbo$\"3gq!*p<'HXB#F27$$\"3$*****\\ilyM;Fbo$\"3gM53X*ee l\"F27$$\"3DLLe*)4D2>Fbo$\"3&*[k%>?XqA\"F27$$\"3emmm;arz@Fbo$\"3;$QOg0 .G4*Fbo7$$\"3.++D\"y%*z7$Fbo$\"3#)4EAwF#R?$Fbo7$$\"3[LL$e9ui2%Fbo$\"38 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