{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 "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 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 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 265 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 266 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 267 "" 1 14 0 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{PARA 4 "" 0 "" {TEXT 276 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 278 22 "(8) Estabilidad lineal" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 277 51 "Ejercicio 08-25 (del E XAMEN ORDINARIO DE 09FEB10)" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 75 "Consid\351rese la familia de m\351todos impl \355citos de RUNGE-KUTTA con dos etapas " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 260 5 " " }{XPPEDIT 18 0 "alpha;" "6# %&alphaG" }{TEXT 261 11 " | " }{XPPEDIT 18 0 "alpha;" "6#%&alp haG" }{TEXT 262 13 " - 1 1 " }}{PARA 4 "" 0 "" {TEXT 263 5 " \+ " }{XPPEDIT 18 0 "beta;" "6#%%betaG" }{TEXT 264 14 " | " } {XPPEDIT 18 0 "beta;" "6#%%betaG" }{TEXT 270 13 " 0 " }} {PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 256 24 "------------ ------------" }}{PARA 4 "" 0 "" {TEXT 257 19 " | " } {XPPEDIT 18 0 "1/4;" "6#*&\"\"\"F$\"\"%!\"\"" }{TEXT 258 10 " \+ " }{XPPEDIT 18 0 "3/4;" "6#*&\"\"$\"\"\"\"\"%!\"\"" }{TEXT 259 1 " " }}{PARA 4 "" 0 "" {TEXT -1 78 "B\372squese el mayor orden alcanzable p or los miembros de esta familia, indicando" }}{PARA 4 "" 0 "" {TEXT -1 16 "los valores de " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT -1 8 " y de " }{XPPEDIT 18 0 "beta;" "6#%%betaG" }{TEXT -1 26 " par a los que se consigue" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 46 "(lo que antecede es Ejercicio del cap\355tulo 7)" }} {PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 67 "Consid \351rese un ejemplo de los de mayor orden y b\372squese en ese caso" } }{PARA 4 "" 0 "" {TEXT -1 36 "la funci\363n de estabilidad del m\351to do" }}}{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 0 21 37 "# desarrollo de la verdadera \+ solucion" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "#y:=unapply(y(x ),x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "#f:=unapply(f(x,y) ,x,y):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f0:=f(x,y(x)):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "f1:=subs(diff(y(x),x)=f(x, y(x)),diff(f0,x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "f2:=s ubs(diff(y(x),x)=f(x,y(x)),diff(f1,x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "f3:=subs(diff(y(x),x)=f(x,y(x)),diff(f2,x)):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "f0:=subs(\{y(x)=y0,x=x0\},f0 ):f0:=expand(f0):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "f1:=su bs(\{y(x)=y0,x=x0\},f1):f1:=expand(f1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "f2:=subs(\{y(x)=y0,x=x0\},f2):f2:=expand(f2):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "f3:=subs(\{y(x)=y0,x=x0\},f3 ):f3:=expand(f3):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 23 "# desar rollo del m\351todo" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "k10: =unapply(f(x0+alpha*h,y0+(alpha-1)*h*kp10(h)+h*kp20(h)),h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "k20:=unapply(f(x0+beta*h,y0+ beta*h*kp10(h)),h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "k100 :=k10(0):k100:=expand(k100):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "k200:=k20(0):k200:=expand(k200):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Fi0:=expand((1/4)*k100+(3/4)*k200):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "k11:=D(k10):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 12 "k21:=D(k20):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "k110:=subs(\{kp10(0)=k100,kp20(0)=k200\},k11(0)):k110:=expand( k110):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "k210:=subs(\{kp10 (0)=k100,kp20(0)=k200\},k21(0)):k210:=expand(k210):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Fi1:=expand((1/4)*k110+(3/4)*k210):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "k12:=D(k11):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "k22:=D(k21):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 98 "k120:=subs(\{D(kp10)(0)=k110,D(kp20)(0)=k210,k p10(0)=k100,kp20(0)=k200\},k12(0)):k120:=expand(k120):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "k220:=subs(\{D(kp10)(0)=k110,D(kp20 )(0)=k210,kp10(0)=k100,kp20(0)=k200\},k22(0)):k220:=expand(k220):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Fi2:=expand((1/4)*k120+(3/4) *k220):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "k13:=D(k12):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "k23:=D(k22):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 140 "k130:=subs(\{(D@@2)(kp10)(0)=k120, (D@@2)(kp20)(0)=k220,D(kp10)(0)=k110,D(kp20)(0)=k210,kp10(0)=k100,kp20 (0)=k200\},k13(0)):k130:=expand(k130):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 140 "k230:=subs(\{(D@@2)(kp10)(0)=k120,(D@@2)(kp20)(0)=k2 20,D(kp10)(0)=k110,D(kp20)(0)=k210,kp10(0)=k100,kp20(0)=k200\},k23(0)) :k230:=expand(k230):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Fi3 :=expand((1/4)*k130+(3/4)*k230):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 24 "# consistencia y orden 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "cond1a:=coeff(Fi0,f(x0,y0))=coeff(f0,f(x0,y0));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond1aG/\"\"\"F&" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# condiciones para el orden 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "cond2a:=coeff(Fi1,D[1](f)(x0,y0))=c oeff((1/2)*f1,D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'c ond2aG/,&*&\"\"%!\"\"%&alphaG\"\"\"F+*(\"\"$F+F(F)%%betaGF+F+#F+\"\"# " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "cond2b:=coeff(coeff(Fi1 ,D[2](f)(x0,y0)),f(x0,y0))=coeff(coeff((1/2)*f1,D[2](f)(x0,y0)),f(x0,y 0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2bG/,&*&\"\"%!\"\"%&alp haG\"\"\"F+*(\"\"$F+F(F)%%betaGF+F+#F+\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "orden2:=solve(\{cond2a\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'orden2G<$/%&alphaG,&*&\"\"$\"\"\"%%betaGF+!\"\"\"\"# F+/F,F," }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# condiciones par a el orden 3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "cond3a:=coe ff(Fi2,D[1,1](f)(x0,y0))=coeff((1/3)*f2,D[1,1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3aG/,&*&\"\"%!\"\"%&alphaG\"\"#\"\"\" *(\"\"$F,F(F)%%betaGF+F,#F,F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "cond3b:=coeff(coeff(Fi2,D[1,2](f)(x0,y0)),f(x0,y0))=coeff(coeff ((1/3)*f2,D[1,2](f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3bG/,&*&\"\"#!\"\"%&alphaGF(\"\"\"*(\"\"$F+F(F)%%betaGF(F +#F(F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "cond3c:=coeff(co eff(Fi2,D[2,2](f)(x0,y0)),f(x0,y0)^2)=coeff(coeff((1/3)*f2,D[2,2](f)(x 0,y0)),f(x0,y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3cG/,&*& \"\"%!\"\"%&alphaG\"\"#\"\"\"*(\"\"$F,F(F)%%betaGF+F,#F,F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "cond3d:=coeff(coeff(Fi2,D[2](f)(x0 ,y0)),D[1](f)(x0,y0))=coeff(coeff((1/3)*f2,D[2](f)(x0,y0)),D[1](f)(x0, y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3dG/,**&#\"\"\"\"\"#F) *$)%&alphaGF*F)F)F)*&#F)F*F)F-F)!\"\"*&F(F)%%betaGF)F)*&#\"\"$F*F)*&F2 F)F-F)F)F)#F)F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "cond3e: =coeff(coeff(Fi2,D[2](f)(x0,y0)^2),f(x0,y0))=coeff(coeff((1/3)*f2,D[2] (f)(x0,y0)^2),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3eG /,**&#\"\"\"\"\"#F)*$)%&alphaGF*F)F)F)*&#F)F*F)F-F)!\"\"*&F(F)%%betaGF )F)*&#\"\"$F*F)*&F2F)F-F)F)F)#F)F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "orden3:=solve(\{cond2a,cond3a,cond3d\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'orden3G<$/%&alphaG\"\"!/%%betaG#\"\"#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 62 "se obtiene orden 3 para lo s valores alpha = 0 y beta = 2/3 " }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# condiciones para el orden 4" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 73 "cond4a:=coeff(Fi3,D[1,1,1](f)(x0,y0))=coeff((1 /4)*f3,D[1,1,1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond 4aG/,&*&\"\"%!\"\"%&alphaG\"\"$\"\"\"*(F+F,F(F)%%betaGF+F,#F,F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "cond4b:=coeff(coeff(Fi3,D[1 ,1,2](f)(x0,y0)),f(x0,y0))=coeff(coeff((1/4)*f3,D[1,1,2](f)(x0,y0)),f( x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4bG/,&*(\"\"*\"\"\" \"\"%!\"\"%%betaG\"\"$F)*(F-F)F*F+%&alphaGF-F)#F-F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "cond4c:=coeff(coeff(Fi3,D[1,2,2](f)(x0,y 0)),f(x0,y0)^2)=coeff(coeff((1/4)*f3,D[1,2,2](f)(x0,y0)),f(x0,y0)^2); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4cG/,&*(\"\"*\"\"\"\"\"%!\" \"%%betaG\"\"$F)*(F-F)F*F+%&alphaGF-F)#F-F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "cond4d:=coeff(coeff(Fi3,D[1,2](f)(x0,y0)),D[1](f) (x0,y0))=coeff(coeff((1/4)*f3,D[1,2](f)(x0,y0)),D[1](f)(x0,y0));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4dG/,**&#\"\"$\"\"#\"\"\"*$)%&a lphaGF)F+F+F+*&#F)F*F+*$)F.F*F+F+!\"\"*&F(F+*&%%betaGF+F.F+F+F+*&#\"\" *F*F+*&F.F+)F6F*F+F+F+#F)\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 145 "cond4e:=coeff(coeff(coeff(Fi3,D[1,2](f)(x0,y0)),D[2](f)(x0,y0 )),f(x0,y0))=coeff(coeff(coeff((1/4)*f3,D[1,2](f)(x0,y0)),D[2](f)(x0,y 0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4eG/,.*&\"\"$ \"\"\")%&alphaGF(F)F)*&#F(\"\"#F)*$)%%betaGF.F)F)F)*&#\"\"*F.F)*&F+F)F 0F)F)F)*&F3F)*&F1F))F+F.F)F)F)*&F-F)*&F1F)F+F)F)F)*&F(F)F8F)!\"\"#\"\" &\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "cond4f:=coeff(co eff(Fi3,D[2,2,2](f)(x0,y0)),f(x0,y0)^3)=coeff(coeff((1/4)*f3,D[2,2,2]( f)(x0,y0)),f(x0,y0)^3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4fG/ ,&*&\"\"%!\"\"%&alphaG\"\"$\"\"\"*(F+F,F(F)%%betaGF+F,#F,F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 145 "cond4g:=coeff(coeff(coeff(F i3,D[2,2](f)(x0,y0)),D[1](f)(x0,y0)),f(x0,y0))=coeff(coeff(coeff((1/4) *f3,D[2,2](f)(x0,y0)),D[1](f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4gG/,**&#\"\"$\"\"#\"\"\"*$)%&alphaGF)F+F+F+*&#F )F*F+*$)F.F*F+F+!\"\"*&F(F+*&%%betaGF+F.F+F+F+*&#\"\"*F*F+*&F.F+)F6F*F +F+F+#F)\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "cond4h:=c oeff(coeff(coeff(Fi3,D[2,2](f)(x0,y0)),D[2](f)(x0,y0)),f(x0,y0)^2)=coe ff(coeff(coeff((1/4)*f3,D[2,2](f)(x0,y0)),D[2](f)(x0,y0)),f(x0,y0)^2); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4hG/,.*&#\"\"$\"\"#\"\"\"*& %%betaGF+%&alphaGF+F+F+*&#\"\"*F*F+*&F.F+)F-F*F+F+F+*&#F1\"\"%F+*&F-F+ )F.F*F+F+F+*&F5F+*$)F.F)F+F+F+*&#F1F6F+*$F8F+F+!\"\"*&#F)F6F+*$F3F+F+F +F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "cond4i:=coeff(coeff (Fi3,D[1,1](f)(x0,y0)),D[2](f)(x0,y0))=coeff(coeff((1/4)*f3,D[1,1](f)( x0,y0)),D[2](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4iG /,**&#\"\"$\"\"%\"\"\"*$)%%betaG\"\"#F+F+F+*&#F)F*F+*$)%&alphaGF/F+F+! \"\"*&#\"\"*F*F+*&F.F+F3F+F+F+*&F(F+*$)F4F)F+F+F+#F+F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "cond4j:=coeff(coeff(Fi3,D[1](f)(x0 ,y0)),D[2](f)(x0,y0)^2)=coeff(coeff((1/4)*f3,D[1](f)(x0,y0)),D[2](f)(x 0,y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4jG/,0*&#\"\"$\"\" #\"\"\"*$)%&alphaGF)F+F+F+*&F)F+)F.F*F+!\"\"*&#\"\"*F*F+*$)%%betaGF*F+ F+F+*&#F)F*F+F7F+F1*&F(F+F.F+F+*&#F)F*F+*&F7F+F.F+F+F1*&F3F+*&F7F+F0F+ F+F+#F+\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "cond4k:=co eff(coeff(Fi3,D[2](f)(x0,y0)^3),f(x0,y0))=coeff(coeff((1/4)*f3,D[2](f) (x0,y0)^3),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4kG/,0 *&#\"\"$\"\"#\"\"\"*$)%&alphaGF)F+F+F+*&F)F+)F.F*F+!\"\"*&#\"\"*F*F+*$ )%%betaGF*F+F+F+*&#F)F*F+F7F+F1*&F(F+F.F+F+*&#F)F*F+*&F7F+F.F+F+F1*&F3 F+*&F7F+F0F+F+F+#F+\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "subs(orden3,\{cond4a,cond4b,cond4c,cond4d,cond4e,cond4f,cond4g,cond4h ,cond4i,cond4j,cond4k\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<)/#\"\" \"\"\"$#F&\"\"%/#\"\"#F'#\"\"&F)/\"\"!#F'F)/F&F(/F+F1/F%F&/#F,\"\"*F( " }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 81 "y no se puede alcanzar o rden 4 , lo que por otra parte era obvio ya que el m\351todo" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 62 "de GAUSS de 2 etapas no est\341 entre los \+ de la familia propuesta" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 66 "Se obt iene orden m\341ximo 3 de una sola manera, para los valores " } {XPPEDIT 18 0 "alpha = 0;" "6#/%&alphaG\"\"!" }{TEXT -1 5 " y " } {XPPEDIT 18 0 "beta = 2/3;" "6#/%%betaG*&\"\"#\"\"\"\"\"$!\"\"" } {TEXT -1 9 " , o sea" }}{PARA 4 "" 0 "" {TEXT -1 14 "para el m\351tod o" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 267 33 " \+ 0 | -1 1" }}{PARA 4 "" 0 "" {TEXT 268 4 " " } {XPPEDIT 18 0 "2/3;" "6#*&\"\"#\"\"\"\"\"$!\"\"" }{TEXT 269 14 " | " }{XPPEDIT 18 0 "2/3;" "6#*&\"\"#\"\"\"\"\"$!\"\"" }{TEXT 273 21 " 0 " }}{PARA 4 "" 0 "" {TEXT -1 12 " ----- ----" }{TEXT 265 44 "--------------------------------------------" }} {PARA 4 "" 0 "" {TEXT 266 21 " | " }{XPPEDIT 18 0 "1 /4;" "6#*&\"\"\"F$\"\"%!\"\"" }{TEXT 271 10 " " }{XPPEDIT 18 0 "3/4;" "6#*&\"\"$\"\"\"\"\"%!\"\"" }{TEXT 272 1 " " }{TEXT -1 0 "" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 30 "# funcion de estabilidad para " }{XPPEDIT 18 0 "alpha = 0;" "6#/%&alphaG\"\"!" }{MPLTEXT 0 21 3 " y " }{XPPEDIT 18 0 "beta = 2/3;" "6#/%%betaG*&\"\"#\"\"\"\"\"$!\"\"" } {MPLTEXT 0 21 5 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "re start:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface(labelin g=false):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=(x,y)->lamb da*y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"xG%\"yG6\"6$%)op eratorG%&arrowGF)*&%'lambdaG\"\"\"9%F/F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "alpha:=0;beta:=2/3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&alphaG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%be taG#\"\"#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 61 "k10:=unapply(f(x0+alpha*h,y0+(alpha-1)*h*kp1(h)+h*k p2(h)),h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k10Gf*6#%\"hG6\"6$%)o peratorG%&arrowGF(*&%'lambdaG\"\"\",(%#y0GF.*&9$F.-%$kp1G6#F2F.!\"\"*& F2F.-%$kp2GF5F.F.F.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "k20:=unapply(f(x0+beta*h,y0+beta*h*kp1(h)),h);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%$k20Gf*6#%\"hG6\"6$%)operatorG%&arrowGF(*&%'lambdaG \"\"\",&%#y0GF.*&#\"\"#\"\"$F.*&9$F.-%$kp1G6#F6F.F.F.F.F(F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "ka1:=unapply(f(x0+alpha*h,y0 +(alpha-1)*h*kp1(h)+h*kp2(h)),h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %$ka1Gf*6#%\"hG6\"6$%)operatorG%&arrowGF(*&%'lambdaG\"\"\",(%#y0GF.*&9 $F.-%$kp1G6#F2F.!\"\"*&F2F.-%$kp2GF5F.F.F.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "ka2:=unapply(f(x0+beta*h,y0+beta*h*kp1(h)),h) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ka2Gf*6#%\"hG6\"6$%)operatorG% &arrowGF(*&%'lambdaG\"\"\",&%#y0GF.*&#\"\"#\"\"$F.*&9$F.-%$kp1G6#F6F.F .F.F.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "test:=solve( \{k1=subs(\{kp1(h)=k1,kp2(h)=k2\},ka1(h)),k2=subs(\{kp1(h)=k1,kp2(h)=k 2\},ka2(h))\},\{k1,k2\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%testG< $/%#k1G,$*,\"\"$\"\"\"%'lambdaGF+%#y0GF+,&F+F+*&F,F+%\"hGF+F+F+,(F*!\" \"*(F*F+F,F+F0F+F2*(\"\"#F+)F,F5F+)F0F5F+F+F2F2/%#k2G,$**F,F+F-F+,&F*F +*(\"\"&F+F,F+F0F+F+F+F1F2F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "k1:=subs(test,k1);k2:=subs(test,k2);simplify(k1+3*k2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k1G,$*,\"\"$\"\"\"%'lambdaGF(%#y0GF(,&F(F (*&F)F(%\"hGF(F(F(,(F'!\"\"*(F'F(F)F(F-F(F/*(\"\"#F()F)F2F()F-F2F(F(F/ F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k2G,$**%'lambdaG\"\"\"%#y0GF( ,&\"\"$F(*(\"\"&F(F'F(%\"hGF(F(F(,(F+!\"\"*(F+F(F'F(F.F(F0*(\"\"#F()F' F3F()F.F3F(F(F0F0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*,\"\"'\"\"\"%' lambdaGF&%#y0GF&,&\"\"#F&*(\"\"$F&F'F&%\"hGF&F&F&,(F,!\"\"*(F,F&F'F&F- F&F/*(F*F&)F'F*F&)F-F*F&F&F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "y1:=expand(y0+h*((1/4)*k1+(3/4)*k2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G,(%#y0G\"\"\"*,\"\"$F'%\"hGF'%'lambdaGF'F&F',(F)! \"\"*(F)F'F+F'F*F'F-*(\"\"#F')F+F0F')F*F0F'F'F-F-*.\"\"*F'F0F-F+F0F&F' F,F-F*F0F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "y1:=collect(s ubs(lambda=z/h,y1),y0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G*&,( \"\"\"F'*(\"\"$F'%\"zGF',(F)!\"\"*&F)F'F*F'F,*&\"\"#F')F*F/F'F'F,F,** \"\"*F'F/F,F*F/F+F,F,F'%#y0GF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "r:=unapply(collect(simplify(y1/y0),z),z):r_particular:=r(z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%-r_particularG,$*(\"\"#!\"\",(\"\" '\"\"\"*&\"#7F+%\"zGF+F+*&\"\"&F+)F.F'F+F+F+,(\"\"$F(*&F3F+F.F+F(*&F'F +F1F+F+F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 45 "# A-estabilidad para alpha = 0 y beta = 2/3" }}} {EXCHG {PARA 4 "" 0 "" {TEXT 274 78 "Este m\351todo no es A-estable, y a que r(z) tiende a -5/4 cuando z tiende a " }{XPPEDIT 18 0 "infi nity;" "6#%)infinityG" }{TEXT 275 3 " " }}}}{MARK "0 3 0" 15 } {VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }