{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 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 270 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 271 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 272 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 273 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 274 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 275 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 276 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 277 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 278 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 279 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 280 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 281 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 282 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "T imes" 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 "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 12 0 0 0 1 2 1 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 280 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 282 22 "(8) Estabilidad lineal" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 281 56 "Ejercicio 08-23 (del E XAMEN EXTRAORDINARIO DE 15JUL09)" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }} {PARA 4 "" 0 "" {TEXT -1 75 "Consid\351rese la familia de m\351todos i mpl\355citos de RUNGE-KUTTA con dos etapas " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 260 15 " 0 | " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT 261 12 " - " }{XPPEDIT 18 0 "a lpha;" "6#%&alphaG" }{TEXT 271 2 " " }}{PARA 4 "" 0 "" {TEXT 262 15 " 2 | " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT 272 14 " \+ 2 - " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }}{PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 256 24 "------------------------" }} {PARA 4 "" 0 "" {TEXT 257 16 " | " }{XPPEDIT 18 0 "1/4;" "6#*&\"\"\"F$\"\"%!\"\"" }{TEXT 258 12 " " }{XPPEDIT 18 0 " 3/4;" "6#*&\"\"$\"\"\"\"\"%!\"\"" }{TEXT 259 1 " " }}{PARA 4 "" 0 "" {TEXT -1 81 "a) B\372squese el mayor orden alcanzable por los miembros de esta familia, indicando" }}{PARA 4 "" 0 "" {TEXT -1 16 "los valore s de " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT -1 26 " para 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 69 "b) Calc \372lese la funci\363n de estabilidad del m\351todo en el caso general ." }}{PARA 4 "" 0 "" {TEXT -1 25 "c) B\372squese un valor de " } {XPPEDIT 18 0 "alpha" "6#%&alphaG" }{TEXT -1 95 " para el que el corre spondiente m\351todo sea\nA-estable, probando, adem\341s, dicha A-esta bilidad. " }}}{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 verdade ra 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 :=subs(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 57 "k10: =unapply(f(x0,y0+alpha*h*kp10(h)-alpha*h*kp20(h)),h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "k20:=unapply(f(x0+2*h,y0+alpha*h*kp 10(h)+(2-alpha)*h*kp20(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 "k 210:=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,kp10(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)*k12 0+(3/4)*k220):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 24 "# consiste ncia y orden 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "cond1a:=c oeff(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))=coeff((1/2)*f1,D[1](f)(x0,y0 ));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2aG/#\"\"$\"\"##\"\"\"F( " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "cond2b:=coeff(coeff(Fi1 ,D[2](f)(x0,y0)),f(x0,y0))=coeff(coeff((1/2)*f1,D[2](f)(x0,y0)),f(x0,y 0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2bG/#\"\"$\"\"##\"\"\"F (" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 55 "s\363lo se obtiene orde n 1 y eso para cualquier valor de " }{XPPEDIT 18 0 "alpha;" "6#%&alph aG" }{MPLTEXT 0 21 5 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 33 "# f uncion de estabilidad general " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interfac e(labeling=false):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=(x ,y)->lambda*y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"xG%\"yG 6\"6$%)operatorG%&arrowGF)*&%'lambdaG\"\"\"9%F/F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "ka1:=unapply(f(x0,y0+alpha*h*kp1(h) -alpha*h*kp2(h)),h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ka1Gf*6#%\" hG6\"6$%)operatorG%&arrowGF(*&%'lambdaG\"\"\",(%#y0GF.*(%&alphaGF.9$F. -%$kp1G6#F3F.F.*(F2F.F3F.-%$kp2GF6F.!\"\"F.F(F(F(" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 63 "ka2:=unapply(f(x0+2*h,y0+alpha*h*kp1(h)+(2-a lpha)*h*kp2(h)),h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ka2Gf*6#%\"h G6\"6$%)operatorG%&arrowGF(*&%'lambdaG\"\"\",(%#y0GF.*(%&alphaGF.9$F.- %$kp1G6#F3F.F.*(,&\"\"#F.F2!\"\"F.F3F.-%$kp2GF6F.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)=k2\},ka2(h))\},\{ k1,k2\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%testG<$/%#k1G,$**%'lam bdaG\"\"\"%#y0GF+,&F+!\"\"*(\"\"#F+F*F+%\"hGF+F+F+,(F+F+*(F0F+F*F+F1F+ F.**F0F+)F*F0F+)F1F0F+%&alphaGF+F+F.F./%#k2G*(F*F+F,F+F2F." }}}{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,$**%'lam bdaG\"\"\"%#y0GF(,&F(!\"\"*(\"\"#F(F'F(%\"hGF(F(F(,(F(F(*(F-F(F'F(F.F( F+**F-F()F'F-F()F.F-F(%&alphaGF(F(F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k2G*(%'lambdaG\"\"\"%#y0GF',(F'F'*(\"\"#F'F&F'%\"hGF'!\"\"**F +F')F&F+F')F,F+F'%&alphaGF'F'F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$* ,\"\"#\"\"\"%'lambdaGF&%#y0GF&,&F%!\"\"*&F'F&%\"hGF&F&F&,(F&F&*(F%F&F' F&F,F&F***F%F&)F'F%F&)F,F%F&%&alphaGF&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\"\"\"**%\"hGF'%'lambdaGF'F&F', (F'F'*(\"\"#F'F*F'F)F'!\"\"**F-F')F*F-F')F)F-F'%&alphaGF'F'F.F'*,F-F.F *F-F&F'F+F.F)F-F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "y1:=co llect(subs(lambda=z/h,y1),y0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y 1G*&,(\"\"\"F'*&%\"zGF',(F'F'*&\"\"#F'F)F'!\"\"*(F,F')F)F,F'%&alphaGF' F'F-F'*(F,F-F)F,F*F-F-F'%#y0GF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "r:=unapply(collect(simplify(y1/y0),z),z):r_general:=r(z);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%*r_generalG,$*(\"\"#!\"\",(F'\"\"\"* &,&*&\"\"%F*%&alphaGF*F*F*F(F*)%\"zGF'F*F**&F'F*F1F*F(F*,(F*F**&F'F*F1 F*F(*(F'F*F0F*F/F*F*F(F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 25 "# pa rece oportuno tomar " }{XPPEDIT 18 0 "alpha = 1/4;" "6#/%&alphaG*&\" \"\"F&\"\"%!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "alpha:= 1/4;num:=numer(r(z));den:=denom(r(z));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&alphaG#\"\"\"\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$numG ,&\"\"#\"\"\"*&F&F'%\"zGF'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ denG,(\"\"#\"\"\"*&\"\"%F'%\"zGF'!\"\"*$)F*F&F'F'" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 41 "z:=x+I*y:assume(x::real):assume(y::real):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "numr:=Re(num);numi:=Im(num );denr:=Re(den);deni:=Im(den);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%n umrG,&\"\"#\"\"\"*&F&F'%#x|irGF'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%numiG,$*&\"\"#\"\"\"%#y|irGF(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%denrG,*\"\"#\"\"\"*&\"\"%F'%#x|irGF'!\"\"*$)F*F&F'F'*$)%#y|ir GF&F'F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%deniG,&*&\"\"%\"\"\"%#y| irGF(!\"\"*(\"\"#F(%#x|irGF(F)F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "simplify(numr^2+numi^2);simplify(denr^2+deni^2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,*\"\"%\"\"\"*&\"\")F%%#x|irGF%!\"\"*& F$F%)F(\"\"#F%F%*&F$F%)%#y|irGF,F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#,4\"\"%\"\"\"*&\"#;F%%#x|irGF%!\"\"*&\"#?F%)F(\"\"#F%F%*&\"#7F%)%#y| irGF-F%F%*&\"\")F%)F(\"\"$F%F)*(F3F%F(F%F0F%F)*$)F(F$F%F%*(F-F%F,F%F0F %F%*$)F1F$F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "borde:=si mplify(numr^2+numi^2-denr^2-deni^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%&bordeG,2*&\"\")\"\"\"%#x|irGF(F(*&\"#;F()F)\"\"#F(!\"\"*&F'F()%#y |irGF-F(F.*&F'F()F)\"\"$F(F(*(F'F(F)F(F0F(F(*$)F)\"\"%F(F.*(F-F(F,F(F0 F(F.*$)F1F8F(F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plo ts):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "implicitplot(borde= 0,x=-40..40,y=-40..40, gridrefine=2);" }}{PARA 13 "" 1 "" {GLPLOT2D 448 448 448 {PLOTDATA 2 "6$-%'CURVESG6$X,%)anythingG6\"6#/%.source_rta bleGX,F'F(6\"[gl'!%\"!!#ao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33333333333333FF4129E4129E41040015511551155133FF089108910890E3FFEB851E B851EBB3FE999999999999A3FFE45832D386EA23FE041C6725BEF8B3FFD7DBF487FCB9 400000000000000003FFDE78861DE7888BFD137BB21137BBB3FFEB851EB851EBBBFE99 9999999999A4003333333333333BFF4129E4129E410400586087A9E7DE2BFF99999999 9999A400999999999999ABFFB6DB6DB6DB6DA400A39C1A39C1A3ABFFAD9E9AD9E9ADA4 010000000000000BFFAD1379E046AD1401026D1A701AD02BFFA34E035A04DA2-%'COLO URG6&%$RGBG$\"\"\"\"\"!$F4F4F5-%+AXESLABELSG6$%#x|irG%#y|irG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 256 "" 0 "" {TEXT 278 74 "Debe hacerse notar que, cuando x<0 , \+ entonces borde <0 , o sea, el borde" }}{PARA 256 "" 0 "" {TEXT 279 65 "de la regi\363n de estabilidad se encuentra en el semiplano Re(z) >0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "r(-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"%\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 263 12 "En el caso " } {XPPEDIT 18 0 "alpha = 1/4;" "6#/%&alphaG*&\"\"\"F&\"\"%!\"\"" }{TEXT 274 65 " la regi\363n de estabilidad contiene todo el semiplano Re( z)<0 ," }}{PARA 4 "" 0 "" {TEXT 273 55 "por lo que el m\351todo es A- estable. Se trata del m\351todo" }}{PARA 4 "" 0 "" {TEXT 264 1 " " }} {PARA 4 "" 0 "" {TEXT 270 14 " 0 | " }{XPPEDIT 18 0 "1/4" "6# *&\"\"\"F$\"\"%!\"\"" }{TEXT 275 7 " - " }{XPPEDIT 18 0 "1/4" "6#* &\"\"\"F$\"\"%!\"\"" }}{PARA 4 "" 0 "" {TEXT 267 15 " 2 | " }{XPPEDIT 18 0 "1/4" "6#*&\"\"\"F$\"\"%!\"\"" }{TEXT 276 6 " " } {XPPEDIT 18 0 "5/4;" "6#*&\"\"&\"\"\"\"\"%!\"\"" }{TEXT 277 3 " " }} {PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 265 10 "----------" }}{PARA 4 "" 0 "" {TEXT 266 14 " | " }{XPPEDIT 18 0 "1/4;" "6#*&\"\"\"F$\"\"%!\"\"" }{TEXT 268 6 " " }{XPPEDIT 18 0 "3/4;" " 6#*&\"\"$\"\"\"\"\"%!\"\"" }{TEXT 269 1 " " }{TEXT -1 0 "" }}}}{MARK " 0 3 0" 15 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }