{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 1 236 0 76 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 48 37 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 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 1 14 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 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 266 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 267 "" 1 18 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 271 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 272 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 273 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 274 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 275 "" 1 18 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 "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Ti mes" 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 }} {SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 265 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 266 48 "(3) Ecuaciones escalares: m\351todos de RUNGE- KUTTA" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 264 56 "Ejercicio 03-15 (del EXAMEN EXTRAORDINARIO de 07JUL12)" }}{PARA 4 " " 0 "" {TEXT -1 56 "\nSe considera el m\351todo de Runge-Kutta de 3 et apas dado " }}{PARA 4 "" 0 "" {TEXT -1 14 "por el tablero" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 256 16 " 1/2 | 0 " }}{PARA 4 "" 0 "" {TEXT 257 18 " 1/2 | 1/2" }}{PARA 4 "" 0 " " {TEXT 260 25 " 1 | 0 1" }}{PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 258 19 "-------------------" }}{PARA 4 "" 0 " " {TEXT 259 34 " | 1/3 1/3 1/3" }}{PARA 4 "" 0 "" {TEXT -1 33 "para el que debe notarse que f( " }{XPPEDIT 18 0 "x[n]; " "6#&%\"xG6#%\"nG" }{TEXT -1 3 " + " }{XPPEDIT 18 0 "1/2;" "6#*&\"\" \"F$\"\"#!\"\"" }{TEXT -1 5 " h , " }{XPPEDIT 18 0 "y[n];" "6#&%\"yG6# %\"nG" }{TEXT -1 3 " ) " }}{PARA 4 "" 0 "" {TEXT -1 56 "B\372squese el orden de consistencia que tiene este m\351todo." }}{PARA 4 "" 0 "" {TEXT -1 68 "B\372squese tambi\351n el orden del m\351todo para el cas o escalar aut\363nomo, " }}{PARA 4 "" 0 "" {TEXT -1 84 "o sea, el caso en el que f(x,y)=f(y).\nCompru\351bese que, para el problema 'test' \+ y'= " }{XPPEDIT 18 0 "lambda;" "6#%'lambdaG" }{TEXT -1 40 " y, el m \351todo\nposee exactamente orden 3." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 269 20 "a) ECUACION COMPLETA" }}}{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 14 "y1:=f(x ,y(x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "y2:=subs(diff(y( x),x)=y1,diff(y1,x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "y3 :=subs(diff(y(x),x)=y1,diff(y2,x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y1:=subs(\{y(x)=y0,x=x0\},y1):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 28 "Y2:=subs(\{y(x)=y0,x=x0\},y2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y3:=subs(\{y(x)=y0,x=x0\},y3):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k1_:=f(x0+1/2*h,y0):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "k2_:=f(x0+1/2*h,y0+1/2*h*k1_ ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "k3_:=f(x0+h,y0+h*k2_) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k1_0:=subs(h=0,k1_):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k2_0:=subs(h=0,k2_):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k3_0:=subs(h=0,k3_):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k11:=diff(k1_,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k21:=diff(k2_,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k31:=diff(k3_,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k110:=subs(h=0,k11):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k210:=subs(h=0,k21):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k310:=subs(h=0,k31):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k12:=diff(k11,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k22:=diff(k21,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k32:=diff(k31,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k120:=subs(h=0,k12):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k220:=subs(h=0,k22):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k320:=subs(h=0,k32):" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 267 27 "condiciones para el orden 1" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Fi_0:=expand(1/3*k1_0+1/3*k2 _0+1/3*k3_0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi_0G-%\"fG6$%#x0G %#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "cond1a:=coeff(Y1,f (x0,y0))=coeff(Fi_0,f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'c ond1aG/\"\"\"F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 268 27 "condiciones p ara el orden 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Fi10:=exp and(1/3*k110+1/3*k210+1/3*k310);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% %Fi10G,&*&#\"\"#\"\"$\"\"\"--&%\"DG6#F*6#%\"fG6$%#x0G%#y0GF*F**&#F*F(F **&--&F.6#F(F0F2F*-F1F2F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "cond2a:=(1/2)*coeff(Y2,D[1](f)(x0,y0))=coeff(Fi10,D[1](f)(x0,y0) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2aG/#\"\"\"\"\"##F(\"\"$ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "cond2b:=(1/2)*coeff(coe ff(Y2,D[2](f)(x0,y0)),f(x0,y0))=coeff(coeff(Fi10,D[2](f)(x0,y0)),f(x0, y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2bG/#\"\"\"\"\"#F&" }} }{EXCHG {PARA 0 "" 0 "" {TEXT 270 20 "b) ECUACION AUTONOMA" }}}{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 21 "f:=unapply(g(y),x,y):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "y1:=f(x,y(x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "y2:=subs(diff(y(x),x)=y1,diff(y1,x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "y3:=subs(diff(y(x),x)=y1,diff(y2,x) ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y1:=subs(\{y(x)=y0,x= x0\},y1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y2:=subs(\{y(x )=y0,x=x0\},y2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y3:=sub s(\{y(x)=y0,x=x0\},y3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 " k1_:=f(x0+1/2*h,y0):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "k2_ :=f(x0+1/2*h,y0+1/2*h*k1_):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k3_:=f(x0,y0+h*k2_):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k1_0:=subs(h=0,k1_):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k2 _0:=subs(h=0,k2_):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k3_0: =subs(h=0,k3_):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k11:=dif f(k1_,h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k21:=diff(k2_, h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k31:=diff(k3_,h):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k110:=subs(h=0,k11):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k210:=subs(h=0,k21):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k310:=subs(h=0,k31):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k12:=diff(k11,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k22:=diff(k21,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k32:=diff(k31,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k120:=subs(h=0,k12):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k220:=subs(h=0,k22):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k320:=subs(h=0,k32):" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 261 27 "condiciones para el orden 1" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Fi_0:=expand(1/3*k1_0+1/3*k2 _0+1/3*k3_0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi_0G-%\"gG6#%#y0G " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "cond1a:=coeff(Y1,f(x0,y 0))=coeff(Fi_0,f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond1a G/\"\"\"F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 262 27 "condiciones para e l orden 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Fi10:=expand(1 /3*k110+1/3*k210+1/3*k310);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi10 G,$*&#\"\"\"\"\"#F(*&--%\"DG6#%\"gG6#%#y0GF(-F/F0F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "#cond2a:=(1/2)*coeff(Y2,D[1](f)(x0, y0))=coeff(Fi10,D[1](f)(x0,y0));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "cond2b:=(1/2)*coeff(coeff(Y2,D[2](f)(x0,y0)),f(x0,y0) )=coeff(coeff(Fi10,D[2](f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2bG/#\"\"\"\"\"#F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 263 28 "condiciones para el orden 3 " }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 41 "Fi20:=expand(1/3*k120+1/3*k220+1/3*k320);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi20G,&*&#\"\"&\"#7\"\"\"*&---%#@@G6$%\"D G\"\"#6#%\"gG6#%#y0GF*)-F4F5F2F*F*F**&#F*\"\"$F**&)--F1F3F5F2F*F8F*F*F *" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "#cond3a:=(1/6)*coeff(Y 3,D[1,1](f)(x0,y0))=(1/2)*coeff(Fi20,D[1,1](f)(x0,y0));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "#cond3b:=(1/6)*coeff(coeff(Y3,D[1, 2](f)(x0,y0)),f(x0,y0))=(1/2)*coeff(coeff(Fi20,D[1,2](f)(x0,y0)),f(x0, y0));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "cond3c:=(1/6)*coe ff(coeff(Y3,D[2,2](f)(x0,y0)),f(x0,y0)^2)=(1/2)*coeff(coeff(Fi20,D[2,2 ](f)(x0,y0)),f(x0,y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3c G/#\"\"\"\"\"'#\"\"&\"#C" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 117 "#cond3d:=(1/6)*coeff(coeff(Y3,D[2](f)(x0,y0)),D[1](f)(x0,y0))=(1/ 2)*coeff(coeff(Fi20,D[2](f)(x0,y0)),D[1](f)(x0,y0));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "cond3e:=(1/6)*coeff(coeff(Y3,D[2](f)(x0, y0)^2),f(x0,y0))=(1/2)*coeff(coeff(Fi20,D[2](f)(x0,y0)^2),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3eG/#\"\"\"\"\"'F&" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 274 16 "b) ECUACION TEST" }}}{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 23 "g:=unapply(lambda*y,y):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "f:=unapply(g(y),x,y):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "y1:=f(x,y(x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "y2:=subs(diff(y(x),x)=y1,diff(y1,x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "y3:=subs(diff(y(x),x)=y1,diff(y2,x) ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y1:=subs(\{y(x)=y0,x= x0\},y1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y2:=subs(\{y(x )=y0,x=x0\},y2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Y2G*&)%'lambdaG \"\"#\"\"\"%#y0GF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y3:=s ubs(\{y(x)=y0,x=x0\},y3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "k1_:=f(x0,y0):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "k2_:= f(x0+1/2*h,y0+1/2*h*k1_):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k3_:=f(x0,y0+h*k2_):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k1_0:=subs(h=0,k1_):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k2 _0:=subs(h=0,k2_):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k3_0: =subs(h=0,k3_):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k11:=dif f(k1_,h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k21:=diff(k2_, h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k31:=diff(k3_,h):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k110:=subs(h=0,k11):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k210:=subs(h=0,k21):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k310:=subs(h=0,k31):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k12:=diff(k11,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k22:=diff(k21,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k32:=diff(k31,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k120:=subs(h=0,k12):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k220:=subs(h=0,k22):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k320:=subs(h=0,k32):" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 271 27 "condiciones para el orden 1" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Fi_0:=expand(1/3*k1_0+1/3*k2 _0+1/3*k3_0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi_0G*&%'lambdaG\" \"\"%#y0GF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "cond1a:=coef f(Y1,y0)=coeff(Fi_0,y0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond1aG /%'lambdaGF&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 272 27 "condiciones para el orden 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Fi10:=expand (1/3*k110+1/3*k210+1/3*k310);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi 10G,$*(\"\"#!\"\"%'lambdaGF'%#y0G\"\"\"F+" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 67 "#cond2a:=(1/2)*coeff(Y2,D[1](f)(x0,y0))=coeff(Fi10, D[1](f)(x0,y0));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "cond2b: =(1/2)*coeff(Y2,y0)=coeff(Fi10,y0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%'cond2bG/,$*&\"\"#!\"\"%'lambdaGF(\"\"\"F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 273 28 "condiciones para el orden 3 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "Fi20:=expand(1/3*k120+1/3*k220+1/3*k320);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi20G,$*(\"\"$!\"\"%'lambdaGF'%#y0G \"\"\"F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "#cond3a:=(1/6)* coeff(Y3,D[1,1](f)(x0,y0))=(1/2)*coeff(Fi20,D[1,1](f)(x0,y0));" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "#cond3b:=(1/6)*coeff(coeff( Y3,D[1,2](f)(x0,y0)),f(x0,y0))=(1/2)*coeff(coeff(Fi20,D[1,2](f)(x0,y0) ),f(x0,y0));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "cond3c:=(1/ 6)*coeff(Y3,y0)=(1/2)*coeff(Fi20,y0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3cG/,$*&\"\"'!\"\"%'lambdaG\"\"$\"\"\"F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 117 "#cond3d:=(1/6)*coeff(coeff(Y3,D[2](f)(x0,y 0)),D[1](f)(x0,y0))=(1/2)*coeff(coeff(Fi20,D[2](f)(x0,y0)),D[1](f)(x0, y0));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "cond3e:=(1/6)*coef f(Y3,y0)=(1/2)*coeff(Fi20,y0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'c ond3eG/,$*&\"\"'!\"\"%'lambdaG\"\"$\"\"\"F&" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 275 40 "funci\363n de estabilidad para este metodo " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 26 "interface(labeling=false):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=(x,y)->lambda*y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"xG%\"yG6\"6$%)operatorG%&arrowGF)*&%'lambd aG\"\"\"9%F/F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k1:=f (x0+(1/2)*h,y0,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k1G*&%'lambda G\"\"\"%#y0GF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "k2:=unapp ly(f(x0+(1/2)*h,y0+(1/2)*h*k1),h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%#k2Gf*6#%\"hG6\"6$%)operatorG%&arrowGF(*&%'lambdaG\"\"\",&%#y0GF.*&# F.\"\"#F.*(9$F.F-F.F0F.F.F.F.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "k3:=unapply(f(x0+h,y0+h*k2(h)),h);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%#k3Gf*6#%\"hG6\"6$%)operatorG%&arrowGF(*&%'lambdaG \"\"\",&%#y0GF.*(9$F.F-F.,&F0F.*&#F.\"\"#F.*(F2F.F-F.F0F.F.F.F.F.F.F(F (F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "y1:=expand(y0+h*((1/ 3)*k1+(1/3)*k2(h)+(1/3)*k3(h)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% #y1G,*%#y0G\"\"\"*(%\"hGF'%'lambdaGF'F&F'F'*&#F'\"\"#F'*()F)F-F')F*F-F 'F&F'F'F'*&#F'\"\"'F'*()F)\"\"$F')F*F6F'F&F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "y1:=collect(subs(lambda=z/h,y1),y0);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G*&,*\"\"\"F'%\"zGF'*&#F'\"\"#F'* $)F(F+F'F'F'*&#F'\"\"'F'*$)F(\"\"$F'F'F'F'%#y0GF'" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 41 "r:=unapply(collect(simplify(y1/y0),z),z);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rGf*6#%\"zG6\"6$%)operatorG%&arro wGF(,*\"\"\"F-9$F-*&#F-\"\"#F-*$)F.F1F-F-F-*&#F-\"\"'F-*$)F.\"\"$F-F-F -F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 15 2" 31 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }