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"" 1 14 0 0 255 0 0 0 0 0 0 0 0 0 0 1 } 0 0 0 -1 4 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE " " -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 268 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 317 22 "(8) Estabilidad lineal" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 316 16 "Ejercicio 08-10 " }} {PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 83 "a) B\372s quense los m\351todos con el mayor orden posible para la familia de RU NGE-KUTTA " }}{PARA 4 "" 0 "" {TEXT -1 32 "impl\355citos del siguiente tablero" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 256 18 " 0 | 0" }}{PARA 4 "" 0 "" {TEXT 257 5 " " } {XPPEDIT 18 0 "c[2]" "6#&%\"cG6#\"\"#" }{TEXT 264 9 " | " } {XPPEDIT 18 0 "a[21]" "6#&%\"aG6#\"#@" }{TEXT 275 8 " " } {XPPEDIT 18 0 "a[22]" "6#&%\"aG6#\"#A" }}{PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 258 24 "------------------------" }}{PARA 4 "" 0 "" {TEXT 259 20 " | " }{XPPEDIT 18 0 "b[1]" "6#&%\"bG 6#\"\"\"" }{TEXT 265 10 " " }{XPPEDIT 18 0 "b[2]" "6#&%\"bG6# \"\"#" }{TEXT 266 1 " " }}{PARA 4 "" 0 "" {TEXT -1 56 "b) Compru\351be se qu\351 se obtiene cuando se fuerza el que " }{XPPEDIT 18 0 "c[2] " "6#&%\"cG6#\"\"#" }{TEXT -1 21 " = 1 , o sea, que las" }}{PARA 4 "" 0 "" {TEXT -1 34 "abscisas implicadas sean 0 y 1 " }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 46 "(lo que antecede es Ej ercicio del cap\355tulo 7)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 84 "c) Para los m\351todos de orden m\341ximo obteni dos, calc\372lese la funci\363n de estabilidad" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 71 "d) Calc\372lese la funci \363n de estabilidad para los m\351todos del apartado b)" }}}{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:=sub s(\{y(x)=y0,x=x0\},y3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 " k1_:=unapply(f(x0,y0),h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "k2_:=unapply(f(x0+c[2]*h,y0+a[2,1]*h*kp1_(h)+a[2,2]*h*kp2_(h)),h): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "k1_0:=k1_(0):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "k2_0:=k2_(0):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "k11:=D(k1_):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 12 "k21:=D(k2_):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "k110:=subs(\{kp1_(0)=k1_0,kp2_(0)=k2_0\},k11(0)):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "k210:=subs(\{kp1_(0)=k1_0,k p2_(0)=k2_0\},k21(0)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "k 12:=D(k11):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "k22:=D(k21): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "k120:=subs(\{D(kp1_)(0) =k110,D(kp2_)(0)=k210,kp1_(0)=k1_0,kp2_(0)=k2_0\},k12(0)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "k220:=subs(\{D(kp1_)(0)=k110,D(kp2_ )(0)=k210,kp1_(0)=k1_0,kp2_(0)=k2_0\},k22(0)):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 263 2 "a)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 27 "condicio nes para el orden 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Fi_0 :=expand(b[1]*k1_0+b[2]*k2_0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%F i_0G,&*&&%\"bG6#\"\"\"F*-%\"fG6$%#x0G%#y0GF*F**&&F(6#\"\"#F*F+F*F*" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "cond1a:=coeff(Y1,f(x0,y0))= coeff(Fi_0,f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond1aG/\" \"\",&&%\"bG6#F&F&&F)6#\"\"#F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(cond1a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/&%\"bG6# \"\"#,&\"\"\"F*&F&6#F*!\"\"/F+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 261 27 "condiciones para el orden 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Fi10:=expand(b[1]*k110+b[2]*k210);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi10G,(*(&%\"bG6#\"\"#\"\"\"--&%\"DG6#F+6#%\"fG6$%#x 0G%#y0GF+&%\"cGF)F+F+**F'F+--&F/F)F1F3F+&%\"aG6$F*F+F+-F2F3F+F+**F'F+F 9F+&F=6$F*F*F+F?F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "con d2a:=(1/2)*coeff(Y2,D[1](f)(x0,y0))=coeff(Fi10,D[1](f)(x0,y0));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2aG/#\"\"\"\"\"#*&&%\"bG6#F(F'& %\"cGF,F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "cond2b:=(1/2)* coeff(coeff(Y2,D[2](f)(x0,y0)),f(x0,y0))=coeff(coeff(Fi10,D[2](f)(x0,y 0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2bG/#\"\"\"\" \"#,&*&&%\"bG6#F(F'&%\"aG6$F(F'F'F'*&F+F'&F/6$F(F(F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "solve(\{cond1a,cond2a,cond2b\},\{b[ 1],c[2],a[2,1]\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%/&%\"cG6#\"\"# ,$*&#\"\"\"F(F,*&F,F,&%\"bGF'!\"\"F,F,/&F/6#F,,&F,F,F.F0/&%\"aG6$F(F,, $*&#F,F(F,*&,&F,F0*(F(F,F.F,&F76$F(F(F,F,F,F.F0F,F0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 262 28 "condiciones para el orden 3 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Fi20:=expand(b[1]*k120+b[2]*k220);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%%Fi20G,4*(&%\"bG6#\"\"#\"\"\"--&%\"D G6$F+F+6#%\"fG6$%#x0G%#y0GF+)&%\"cGF)F*F+F+*.F*F+F'F+F7F+--&F/6$F+F*F1 F3F+&%\"aG6$F*F+F+-F2F3F+F+*.F*F+F'F+F7F+F:F+&F?6$F*F*F+FAF+F+**F'F+-- &F/FDF1F3F+)F>F*F+)FAF*F+F+*.F*F+F'F+FFF+F>F+FJF+FCF+F+**F'F+FFF+)FCF* F+FJF+F+*.F*F+F'F+--&F/F)F1F3F+FCF+--&F/6#F+F1F3F+F7F+F+*.F*F+F'F+)FOF *F+FCF+F>F+FAF+F+*,F*F+F'F+FWF+FMF+FAF+F+" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 76 "cond3a:=(1/6)*coeff(Y3,D[1,1](f)(x0,y0))=(1/2)*coef f(Fi20,D[1,1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3a G/#\"\"\"\"\"',$*&#F'\"\"#F'*&&%\"bG6#F,F')&%\"cGF0F,F'F'F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "cond3b:=(1/6)*coeff(coeff(Y 3,D[1,2](f)(x0,y0)),f(x0,y0))=(1/2)*coeff(coeff(Fi20,D[1,2](f)(x0,y0)) ,f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3bG/#\"\"\"\"\"$ ,&*(&%\"bG6#\"\"#F'&%\"cGF-F'&%\"aG6$F.F'F'F'*(F+F'F/F'&F26$F.F.F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "cond3c:=(1/6)*coeff(coef f(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#>%'cond3cG/#\"\" \"\"\"',(*&#F'\"\"#F'*&&%\"bG6#F,F')&%\"aG6$F,F'F,F'F'F'*(F.F'F2F'&F36 $F,F,F'F'*&F+F'*&F.F')F6F,F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "cond3d:=(1/6)*coeff(coeff(Y3,D[2](f)(x0,y0)),D[1](f) (x0,y0))=(1/2)*coeff(coeff(Fi20,D[2](f)(x0,y0)),D[1](f)(x0,y0));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3dG/#\"\"\"\"\"'*(&%\"bG6#\"\"# F'&%\"cGF,F'&%\"aG6$F-F-F'" }}}{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)*co eff(coeff(Fi20,D[2](f)(x0,y0)^2),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3eG/#\"\"\"\"\"',&*(&%\"bG6#\"\"#F'&%\"aG6$F.F'F '&F06$F.F.F'F'*&F+F')F2F.F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "solucion:=solve(\{cond1a,cond2a,cond2b,cond3a,cond3b,cond3c,cond 3d,cond3e\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)solucionG<'/&%\"cG 6#\"\"##F*\"\"$/&%\"bG6#\"\"\"#F1\"\"%/&F/F)#F,F3/&%\"aG6$F*F1#F1F,/&F 96$F*F*F;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 269 69 "Es decir, existe un a \372nica soluci\363n de orden 3 . Se trata del m\351todo" }}{PARA 0 "" 0 "" {TEXT 276 19 "dado por el tablero" }}{PARA 4 "" 0 "" {TEXT 277 18 " 0 | 0" }}{PARA 4 "" 0 "" {TEXT 278 5 " " } {XPPEDIT 18 0 "2/3" "6#*&\"\"#\"\"\"\"\"$!\"\"" }{TEXT 281 9 " | \+ " }{XPPEDIT 18 0 "1/3" "6#*&\"\"\"F$\"\"$!\"\"" }{TEXT 284 9 " \+ " }{XPPEDIT 18 0 "1/3" "6#*&\"\"\"F$\"\"$!\"\"" }}{PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 279 24 "------------------------" }} {PARA 4 "" 0 "" {TEXT 280 17 " | " }{XPPEDIT 18 0 "1/4" "6#*&\"\"\"F$\"\"%!\"\"" }{TEXT 282 10 " " }{XPPEDIT 18 0 "3/ 4" "6#*&\"\"$\"\"\"\"\"%!\"\"" }{TEXT 283 1 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 289 2 "b)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 288 16 "forzando a que " }{XPPEDIT 18 0 "c[2]" "6#&%\"cG6#\"\"#" }{TEXT 290 6 " = 1 \+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "solucion1:=solve(\{cond 1a,cond2a,cond2b,c[2]=1\},\{c[2],a[2,1],b[1],b[2]\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*solucion1G<&/&%\"cG6#\"\"#\"\"\"/&%\"bG6#F+#F+F */&F.F)F0/&%\"aG6$F*F+,&F+F+&F56$F*F*!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 291 53 "Se obtiene la familia de orden 2 dada por el tablero" } }{PARA 4 "" 0 "" {TEXT 292 18 " 0 | 0" }}{PARA 4 "" 0 "" {TEXT 293 16 " 1 | " }{XPPEDIT 18 0 "1-a[22]" "6#,&\"\"\"F$ &%\"aG6#\"#A!\"\"" }{TEXT 298 9 " " }{XPPEDIT 18 0 "a[22]" "6# &%\"aG6#\"#A" }}{PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 294 24 "------------------------" }}{PARA 4 "" 0 "" {TEXT 295 27 " \+ | " }{XPPEDIT 18 0 "1/2" "6#*&\"\"\"F$\"\"#!\"\"" } {TEXT 296 14 " " }{XPPEDIT 18 0 "1/2" "6#*&\"\"\"F$\"\"#! \"\"" }{TEXT 297 1 " " }}{PARA 0 "" 0 "" {TEXT 299 25 " uno de cuyos m \351todos es " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "solucion2:=subs(a[2,2]=1/2,solucion1) union \{a[ 2,2]=1/2\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*solucion2G<'/&%\"cG6 #\"\"#\"\"\"/&%\"bG6#F+#F+F*/&F.F)F0/&%\"aG6$F*F*F0/&F56$F*F+F0" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 310 46 "el conocido como LOBATTO IIIA \+ de 2 etapas" }}{PARA 4 "" 0 "" {TEXT 300 18 " 0 | 0" }} {PARA 4 "" 0 "" {TEXT 301 16 " 1 | " }{XPPEDIT 18 0 "1/2" " 6#*&\"\"\"F$\"\"#!\"\"" }{TEXT 305 9 " " }{XPPEDIT 18 0 "1/2" "6#*&\"\"\"F$\"\"#!\"\"" }}{PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 302 24 "------------------------" }}{PARA 4 "" 0 "" {TEXT 303 17 " | " }{XPPEDIT 18 0 "1/2" "6#*&\"\"\"F$\"\"#!\"\"" } {TEXT 304 10 " " }{XPPEDIT 18 0 "1/2" "6#*&\"\"\"F$\"\"#!\"\" " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 270 2 "c)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 267 23 "funci\363n de estabilid ad " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=(x,y)->lambda*y; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"xG%\"yG6\"6$%)operato rG%&arrowGF)*&%'lambdaG\"\"\"9%F/F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "ka1:=unapply(f(x0,y0),h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ka1Gf*6#%\"hG6\"6$%)operatorG%&arrowGF(*&%'lambdaG\" \"\"%#y0GF.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "ka2:=u napply(f(x0+c[2]*h,y0+a[2,1]*h*kp1(h)+a[2,2]*h*kp2(h)),h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ka2Gf*6#%\"hG6\"6$%)operatorG%&arrowGF(*& %'lambdaG\"\"\",(%#y0GF.*(&%\"aG6$\"\"#F.F.9$F.-%$kp1G6#F6F.F.*(&F36$F 5F5F.F6F.-%$kp2GF9F.F.F.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "test:=solve(\{k1=subs(\{kp1(h)=k1,kp2(h)=k2\},ka1(h)),k2=subs( \{kp1(h)=k1,kp2(h)=k2\},ka2(h))\},\{k1,k2\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%testG<$/%#k1G*&%'lambdaG\"\"\"%#y0GF*/%#k2G,$**F)F*F +F*,&F*F**(F)F*&%\"aG6$\"\"#F*F*%\"hGF*F*F*,&F*!\"\"*(F)F*&F36$F5F5F*F 6F*F*F8F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "k1:=subs(test, k1);k2:=subs(test,k2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k1G*&%'la mbdaG\"\"\"%#y0GF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k2G,$**%'lamb daG\"\"\"%#y0GF(,&F(F(*(F'F(&%\"aG6$\"\"#F(F(%\"hGF(F(F(,&F(!\"\"*(F'F (&F-6$F/F/F(F0F(F(F2F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "y 1:=expand(y0+h*(b[1]*k1+b[2]*k2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%#y1G,*%#y0G\"\"\"**%\"hGF'&%\"bG6#F'F'%'lambdaGF'F&F'F'*,F)F'&F+6#\" \"#F'F-F'F&F',&F'!\"\"*(F-F'&%\"aG6$F1F1F'F)F'F'F3F3*.F/F'F-F1F&F'F2F3 &F66$F1F'F'F)F1F3" }}}{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'*&&%\"bG6#F'F'%\"zGF'F'*(&F*6#\"\"#F'F,F',&F'!\"\"*&F,F' &%\"aG6$F0F0F'F'F2F2**F.F'F,F0F1F2&F56$F0F'F'F2F'%#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$%)operat orG%&arrowGF(,$*&,(\"\"\"F/*&,&*&&%\"bG6#F/F/&%\"aG6$\"\"#F9F/!\"\"*&& F46#F9F/&F76$F9F/F/F/F/)9$F9F/F/*&,(F6F:F3F/F " 0 "" {MPLTEXT 1 0 45 "r1:=unapply(simplify(subs(solucion,r(z))),z);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#r1Gf*6#%\"zG6\"6$%)operatorG%&arrow GF(,$*&#\"\"\"\"\"#F/*&,(\"\"'F/*$)9$F0F/F/*&\"\"%F/F6F/F/F/,&\"\"$!\" \"F6F/F;F/F;F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 272 88 "lo es de l a soluci\363n de orden 3 obtenida. Ahora, el dominio de estabilidad, compuesto " }}{PARA 0 "" 0 "" {TEXT 286 13 "por los z = " }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT 273 69 " h tales que el m\363dulo de r1(z) sea inferior a 1 no ser\341 todo el" }}{PARA 0 "" 0 "" {TEXT 274 84 "semiplano de parte real negativa, ya que la funci\363n d e estabilidad tiende a infinito" }}{PARA 0 "" 0 "" {TEXT 287 86 "cuand o z tiende a infinito en cualquier direcci\363n. O sea, el m\351todo no es A-estable" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 307 2 "d)" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 306 42 "funci\363n de estabilidad para m \351todos de b) " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "r2:=una pply(simplify(subs(solucion1,r(z))),z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#r2Gf*6#%\"zG6\"6$%)operatorG%&arrowGF(,$*&#\"\"\"\"\"#F/*&,,F 0!\"\"*(F0F/)9$F0F/&%\"aG6$F0F0F/F/*$F5F/F3*&F0F/F6F/F3*(F0F/F6F/F7F/F /F/,&F/F3*&F6F/F7F/F/F3F/F/F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 308 75 "y, a priori, nada podemos decir de la A-estabilidad . Sin emb argo, para el" }}{PARA 0 "" 0 "" {TEXT 309 35 "m\351todo LOBATTO IIIA de 2 etapas" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "r3:=unap ply(simplify(subs(solucion2,r(z))),z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#r3Gf*6#%\"zG6\"6$%)operatorG%&arrowGF(,$*&,&\"\"#\"\"\"9$F0F0 ,&F/!\"\"F1F0F3F3F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 311 50 "el dominio de estabilidad, c ompuesto por los z = " }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT 312 35 " h tales que el m\363dulo de r3(z) " }}{PARA 0 "" 0 "" {TEXT 313 88 "sea inferior a 1 , estar\341 formado por los valores de z que disten menos del punto -2" }}{PARA 0 "" 0 "" {TEXT 314 86 "q ue del punto 2 . Esto corresponde al semiplano de parte real negativa , por lo que el" }}{PARA 0 "" 0 "" {TEXT 315 30 "m\351todo estudiado e s A-estable" }}}}{MARK "0 3 0" 15 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }