{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 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 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 1 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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 "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 }} {SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 285 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 286 48 "(3) Ecuaciones escalares: m\351todos de RUNGE- KUTTA" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 284 15 "Ejercicio 03-06" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 80 "Consid\351rese la familia de m\351todos de Runge-Kutta de 3 etapas y expl\355citos dados " }}{PARA 4 "" 0 "" {TEXT -1 14 "por e l tablero" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 256 13 " 0 | " }}{PARA 4 "" 0 "" {TEXT 257 7 " " } {XPPEDIT 18 0 "c[2]" "6#&%\"cG6#\"\"#" }{TEXT 270 8 " | " } {XPPEDIT 18 0 "a[2,1]" "6#&%\"aG6$\"\"#\"\"\"" }}{PARA 4 "" 0 "" {TEXT 260 7 " " }{XPPEDIT 18 0 "c[3]" "6#&%\"cG6#\"\"$" }{TEXT 271 8 " | " }{XPPEDIT 18 0 "a[3,1]" "6#&%\"aG6$\"\"$\"\"\"" } {TEXT 272 6 " " }{XPPEDIT 18 0 "a[3,2]" "6#&%\"aG6$\"\"$\"\"#" }} {PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 258 29 "------------ -----------------" }}{PARA 4 "" 0 "" {TEXT 259 45 " | \+ 0 0 " }{XPPEDIT 18 0 "b[3]" "6#&%\"bG6#\"\"$" }} {PARA 4 "" 0 "" {TEXT -1 40 "a) Para qu\351 valores de los par\341metr os " }{TEXT 273 1 " " }{XPPEDIT 18 0 "c[2]" "6#&%\"cG6#\"\"#" } {TEXT -1 2 " ," }{TEXT 274 1 " " }{XPPEDIT 18 0 "c[3]" "6#&%\"cG6#\"\" $" }{TEXT -1 3 " , " }{XPPEDIT 18 0 "a[2,1]" "6#&%\"aG6$\"\"#\"\"\"" } {TEXT -1 3 " , " }{XPPEDIT 18 0 "a[3,1]" "6#&%\"aG6$\"\"$\"\"\"" } {TEXT -1 3 " , " }{TEXT 275 1 " " }{XPPEDIT 18 0 "a[3,2]" "6#&%\"aG6$ \"\"$\"\"#" }{TEXT -1 5 " y " }{XPPEDIT 18 0 "b[3]" "6#&%\"bG6#\"\"$ " }{TEXT -1 14 " los m\351todos " }}{PARA 4 "" 0 "" {TEXT -1 16 "son \+ de orden 2 ?" }}{PARA 4 "" 0 "" {TEXT -1 76 "b) De los m\351todos ante riores, cu\341les minimizan adem\341s el t\351rmino del error ?" }} {PARA 4 "" 0 "" {TEXT -1 38 "c) Existen valores de los par\341metros \+ " }{TEXT 276 1 " " }{XPPEDIT 18 0 "c[2]" "6#&%\"cG6#\"\"#" }{TEXT -1 2 " ," }{TEXT 277 1 " " }{XPPEDIT 18 0 "c[3]" "6#&%\"cG6#\"\"$" } {TEXT -1 3 " , " }{XPPEDIT 18 0 "a[2,1]" "6#&%\"aG6$\"\"#\"\"\"" } {TEXT -1 3 " , " }{XPPEDIT 18 0 "a[3,1]" "6#&%\"aG6$\"\"$\"\"\"" } {TEXT -1 3 " , " }{TEXT 278 1 " " }{XPPEDIT 18 0 "a[3,2]" "6#&%\"aG6$ \"\"$\"\"#" }{TEXT -1 5 " y " }{XPPEDIT 18 0 "b[3]" "6#&%\"bG6#\"\"$ " }{TEXT -1 19 " para los que los " }}{PARA 4 "" 0 "" {TEXT -1 25 "m \351todos sean de orden 3 ?" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 40 "(desde aqu\355 es Ejercicio del cap\355tulo 8) " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 76 "d) Pa ra la familia de m\351todos propuesta, calc\372lese la funci\363n de e stabilidad" }}{PARA 4 "" 0 "" {TEXT -1 15 "en t\351rminos de " }{TEXT 279 1 " " }{XPPEDIT 18 0 "c[2]" "6#&%\"cG6#\"\"#" }{TEXT -1 2 " ," } {TEXT 280 1 " " }{XPPEDIT 18 0 "c[3]" "6#&%\"cG6#\"\"$" }{TEXT -1 3 " \+ , " }{XPPEDIT 18 0 "a[2,1]" "6#&%\"aG6$\"\"#\"\"\"" }{TEXT -1 3 " , " }{XPPEDIT 18 0 "a[3,1]" "6#&%\"aG6$\"\"$\"\"\"" }{TEXT -1 3 " , " } {TEXT 281 1 " " }{XPPEDIT 18 0 "a[3,2]" "6#&%\"aG6$\"\"$\"\"#" }{TEXT -1 5 " y " }{XPPEDIT 18 0 "b[3]" "6#&%\"bG6#\"\"$" }{TEXT -1 32 " . \+ Calc\372lese esta misma funci\363n " }}{PARA 4 "" 0 "" {TEXT -1 91 "pa ra los m\351todos de orden 2 , los que minimizan el error y los de ord en 3 que, en su caso, " }}{PARA 4 "" 0 "" {TEXT -1 24 "se hayan podido obtener." }}}{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,dif f(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 14 "k1_:=f(x0,y0):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "k2_:=f(x0+c[2]*h,y0+a[2,1]*h*k1_):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "k3_:=f(x0+c[3]*h,y0+a[3,1]*h*k1_+a[3,2]*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 264 2 "a)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 261 27 "condiciones para el orden 1" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 38 "Fi_0:=expand(0*k1_0+0*k2_0+b[3]*k3_0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi_0G*&&%\"bG6#\"\"$\"\"\"-%\"fG6$%#x0G%#y0G F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "cond1a:=coeff(Y1,f(x0 ,y0))=coeff(Fi_0,f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond 1aG/\"\"\"&%\"bG6#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 262 27 "condi ciones para el orden 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "F i10:=expand(0*k110+0*k210+b[3]*k310);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi10G,(*(&%\"bG6#\"\"$\"\"\"--&%\"DG6#F+6#%\"fG6$%#x0G%#y0GF+&% \"cGF)F+F+**F'F+--&F/6#\"\"#F1F3F+&%\"aG6$F*F+F+-F2F3F+F+**F'F+F9F+&F? 6$F*F=F+FAF+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/#\"\"\"\"\"#*&&%\"bG6#\"\"$F'&%\"cGF ,F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "cond2b:=(1/2)*coeff( coeff(Y2,D[2](f)(x0,y0)),f(x0,y0))=coeff(coeff(Fi10,D[2](f)(x0,y0)),f( x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2bG/#\"\"\"\"\"#,&* &&%\"bG6#\"\"$F'&%\"aG6$F.F'F'F'*&F+F'&F06$F.F(F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "sol1:=solve(\{cond1a,cond2a,cond2b\},\{b[ 3],c[3],a[3,1]\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%sol1G<%/&%\"c G6#\"\"$#\"\"\"\"\"#/&%\"bGF)F,/&%\"aG6$F*F,,&F+F,&F36$F*F-!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "b[3]:=subs(sol1,b[3]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"bG6#\"\"$\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "c[3]:=subs(sol1,c[3]);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>&%\"cG6#\"\"$#\"\"\"\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "a[3,1]:=subs(sol1,a[3,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"aG6$\"\"$\"\"\",&#F(\"\"#F(&F%6$F'F+!\"\"" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 265 2 "b)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 263 44 "condiciones para el orden 3 o para el error " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "Fi20:=expand(0*k120+0*k220+b[3]*k32 0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi20G,,*&#\"\"\"\"\"%F(--&% \"DG6$F(F(6#%\"fG6$%#x0G%#y0GF(F(*&#F(\"\"#F(*&--&F-6$F(F6F/F1F(-F0F1F (F(F(*&F'F(*&--&F-6$F6F6F/F1F()F " 0 "" {MPLTEXT 1 0 76 "cond3a:=(1/6)*coeff(Y3, D[1,1](f)(x0,y0))=(1/2)*coeff(Fi20,D[1,1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3aG/#\"\"\"\"\"'#F'\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "cond3b:=(1/6)*coeff(coeff(Y3,D[1,2](f)(x 0,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/#\"\"\"\"\"$#F'\"\"%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "cond3c:=(1/6)*coeff(coeff(Y 3,D[2,2](f)(x0,y0)),f(x0,y0)^2)=(1/2)*coeff(coeff(Fi20,D[2,2](f)(x0,y0 )),f(x0,y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3cG/#\"\"\" \"\"'#F'\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "cond3d:=( 1/6)*coeff(coeff(Y3,D[2](f)(x0,y0)),D[1](f)(x0,y0))=(1/2)*coeff(coeff( Fi20,D[2](f)(x0,y0)),D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3dG/#\"\"\"\"\"'*&&%\"aG6$\"\"$\"\"#F'&%\"cG6#F.F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "cond3e:=(1/6)*coeff(coeff(Y 3,D[2](f)(x0,y0)^2),f(x0,y0))=(1/2)*coeff(coeff(Fi20,D[2](f)(x0,y0)^2) ,f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3eG/#\"\"\"\"\"' *&&%\"aG6$\"\"$\"\"#F'&F+6$F.F'F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 283 2 "c)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 282 23 "minimizaci\363n del error " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "sol2:=solve(\{co nd3d,cond3e\},\{a[2,1],a[3,2]\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %%sol2G<$/&%\"aG6$\"\"#\"\"\"&%\"cG6#F*/&F(6$\"\"$F*,$*&#F+\"\"'F+*&F+ F+F,!\"\"F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "a[2,1]:=su bs(sol2,a[2,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"aG6$\"\"#\"\" \"&%\"cG6#F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "a[3,2]:=sub s(sol2,a[3,2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"aG6$\"\"$\"\"# ,$*&#\"\"\"\"\"'F,*&F,F,&%\"cG6#F(!\"\"F,F," }}}{EXCHG {PARA 0 "" 0 " " {TEXT 266 2 "d)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 267 23 "funci\363n \+ de estabilidad " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface(labeling=fals e):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=(x,y)->lambda*y; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"xG%\"yG6\"6$%)operato rG%&arrowGF)*&%'lambdaG\"\"\"9%F/F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "k1_:=f(x0,y0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ k1_G*&%'lambdaG\"\"\"%#y0GF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "k2_:=f(x0+c[2]*h,y0+a[2,1]*h*k1_);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k2_G*&%'lambdaG\"\"\",&%#y0GF'**&%\"aG6$\"\"#F'F'%\"hGF'F&F'F )F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "k3_:=f(x0+c[3]*h ,y0+a[3,1]*h*k1_+a[3,2]*h*k2_);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ k3_G*&%'lambdaG\"\"\",(%#y0GF'**&%\"aG6$\"\"$F'F'%\"hGF'F&F'F)F'F'**&F ,6$F.\"\"#F'F/F'F&F',&F)F'**&F,6$F3F'F'F/F'F&F'F)F'F'F'F'F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "y1:=expand(y0+h*(0*k1_+0*k2_ +b[3]*k3_));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G,,%#y0G\"\"\"**% \"hGF'&%\"bG6#\"\"$F'%'lambdaGF'F&F'F'*,)F)\"\"#F'F*F')F.F1F'&%\"aG6$F -F'F'F&F'F'*,F0F'F*F'F2F'&F46$F-F1F'F&F'F'*.)F)F-F'F*F')F.F-F'F7F'&F46 $F1F'F'F&F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "y1:=collec t(subs(lambda=z/h,y1),y0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G*& ,,\"\"\"F'*&&%\"bG6#\"\"$F'%\"zGF'F'*(F)F')F-\"\"#F'&%\"aG6$F,F'F'F'*( F)F'F/F'&F26$F,F0F'F'**F)F')F-F,F'F5F'&F26$F0F'F'F'F'%#y0GF'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "r:=unapply(collect(simplify( y1/y0),z),z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rGf*6#%\"zG6\"6$% )operatorG%&arrowGF(,*\"\"\"F-**&%\"bG6#\"\"$F-)9$F2F-&%\"aG6$F2\"\"#F -&F66$F8F-F-F-*&,&*&F/F-&F66$F2F-F-F-*&F/F-F5F-F-F-)F4F8F-F-*&F/F-F4F- F-F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 268 51 "funci\363n de estabi lidad para los metodos de orden 2 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "r2:=unapply(subs(\{c[3]=1/2,a[3,1]=1/2-a[3,2],b[3]=1 \},r(z)),z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#r2Gf*6#%\"zG6\"6$%) operatorG%&arrowGF(,*\"\"\"F-*()9$\"\"$F-&%\"aG6$F1\"\"#F-&F36$F5F-F-F -*&#F-F5F-*$)F0F5F-F-F-F0F-F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 269 63 "funci\363n de estabilidad para los metodos que minimizan el er ror " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "r3:=unapply(subs(\{ a[2,1]=c[2],a[3,2]=1/6/c[2]\},r2(z)),z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#r3Gf*6#%\"zG6\"6$%)operatorG%&arrowGF(,*\"\"\"F-*&#F-\"\"'F-* $)9$\"\"$F-F-F-*&#F-\"\"#F-*$)F3F7F-F-F-F3F-F(F(F(" }}}}{MARK "0 0 0" 9 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }