{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 18 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 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 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 1 24 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 18 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 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 281 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 282 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 283 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 284 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 285 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 286 "" 1 14 0 0 84 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 287 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 288 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 289 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 290 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 291 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 292 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 293 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 294 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 295 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 296 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 297 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 298 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 " " 0 1 0 0 2 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 50 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 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 269 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 297 22 "(8) Estabilidad lineal" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 296 16 "Ejercicio 08-11 " }} {PARA 4 "" 0 "" {TEXT -1 84 "\na) B\372squense los m\351todos con el m ayor orden posible para la familia de RUNGE-KUTTA " }}{PARA 4 "" 0 "" {TEXT -1 32 "impl\355citos del siguiente tablero" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 256 18 " 1 | 1" }} {PARA 4 "" 0 "" {TEXT 257 5 " " }{XPPEDIT 18 0 "c[2]" "6#&%\"cG6# \"\"#" }{TEXT 265 18 " | 0 " }{XPPEDIT 18 0 "a[22]" "6#&% \"aG6#\"#A" }}{PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 258 24 "------------------------" }}{PARA 4 "" 0 "" {TEXT 259 18 " \+ | " }{XPPEDIT 18 0 "b[1]" "6#&%\"bG6#\"\"\"" }{TEXT 266 8 " \+ " }{XPPEDIT 18 0 "b[2]" "6#&%\"bG6#\"\"#" }{TEXT 267 1 " " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 68 "b) Pru \351bese que, entre los m\351todos obtenidos, se encuentra el m\351tod o" }}{PARA 4 "" 0 "" {TEXT -1 24 "de GAUSS de 1 sola etapa" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 46 "(lo que antecede \+ es Ejercicio del cap\355tulo 7)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 4 "" 0 "" {TEXT -1 68 "c) Para los m\351todos obtenidos, 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 esta bilidad para el citado m\351todo de GAUSS, " }}{PARA 4 "" 0 "" {TEXT -1 30 "y compru\351bese que es A-estable" }}}{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:=s ubs(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 37 "k1_:=unapply(f (x0+h,y0+h*kp1_(h)),h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 " k2_:=unapply(f(x0+c[2]*h,y0+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(\{k p1_(0)=k1_0,kp2_(0)=k2_0\},k11(0)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "k210:=subs(\{kp1_(0)=k1_0,kp2_(0)=k2_0\},k21(0)):" }} }{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 79 "k120:=subs(\{D(kp1_)(0)=k110,D(kp2_)(0)=k210,k p1_(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 "condiciones 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#>%%Fi_0G,&*&&%\"bG6#\" \"\"F*-%\"fG6$%#x0G%#y0GF*F**&&F(6#\"\"#F*F+F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "cond1a:=coeff(Y1,f(x0,y0))=coeff(Fi_0,f(x0,y0 ));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond1aG/\"\"\",&&%\"bG6#F&F& &F)6#\"\"#F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(cond1 a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/&%\"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#\"\"\"F*--&%\"DGF)6#%\"fG6$%#x0G%#y0GF*F**(F'F*--&F.6#\"\"#F/F 1F*-F0F1F*F**(&F(F8F*F+F*&%\"cGF8F*F***F " 0 "" {MPLTEXT 1 0 66 "cond2a:=(1/2)*coeff(Y2,D[1 ](f)(x0,y0))=coeff(Fi10,D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2aG/#\"\"\"\"\"#,&&%\"bG6#F'F'*&&F+6#F(F'&%\"cGF/F'F'" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "cond2b:=(1/2)*coeff(coeff(Y 2,D[2](f)(x0,y0)),f(x0,y0))=coeff(coeff(Fi10,D[2](f)(x0,y0)),f(x0,y0)) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2bG/#\"\"\"\"\"#,&&%\"bG6# F'F'*&&F+6#F(F'&%\"aG6$F(F(F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "solucion:=solve(\{cond1a,cond2a,cond2b\},\{b[1],c[2],a[2,2]\}) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)solucionG<%/&%\"cG6#\"\"#,$*&# \"\"\"F*F.*&,&F.!\"\"*&F*F.&%\"bGF)F.F.F.F3F1F.F./&F46#F.,&F.F.F3F1/&% \"aG6$F*F*F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 262 28 "condiciones para el orden 3 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Fi20:=expan d(b[1]*k120+b[2]*k220);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%Fi20G,6* &&%\"bG6#\"\"\"F*--&%\"DG6$F*F*6#%\"fG6$%#x0G%#y0GF*F***\"\"#F*F'F*--& F.6$F*F6F0F2F*-F1F2F*F**(F'F*--&F.6$F6F6F0F2F*)F;F6F*F***F6F*F'F*--&F. 6#F6F0F2F*--&F.F)F0F2F*F***F6F*F'F*)FCF6F*F;F*F**(&F(FFF*F+F*)&%\"cGFF F6F*F**.F6F*FMF*FOF*F7F*&%\"aGF@F*F;F*F***FMF*)FRF6F*FAF*F=F*F**.F6F*F MF*FCF*FRF*FGF*FOF*F**,F6F*FMF*FKF*FUF*F;F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "cond3a:=(1/6)*coeff(Y3,D[1,1](f)(x0,y0))=(1/2)*c oeff(Fi20,D[1,1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'con d3aG/#\"\"\"\"\"',&*&#F'\"\"#F'&%\"bG6#F'F'F'*&F+F'*&&F.6#F,F')&%\"cGF 3F,F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "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));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3b G/#\"\"\"\"\"$,&&%\"bG6#F'F'*(&F+6#\"\"#F'&%\"cGF/F'&%\"aG6$F0F0F'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'F'*&F+F'*&&F.6#F,F')&%\"aG6$F,F,F,F'F 'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "cond3d:=(1/6)*coeff (coeff(Y3,D[2](f)(x0,y0)),D[1](f)(x0,y0))=(1/2)*coeff(coeff(Fi20,D[2]( f)(x0,y0)),D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond 3dG/#\"\"\"\"\"',&&%\"bG6#F'F'*(&F+6#\"\"#F'&%\"cGF/F'&%\"aG6$F0F0F'F' " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "cond3e:=(1/6)*coeff(co eff(Y3,D[2](f)(x0,y0)^2),f(x0,y0))=(1/2)*coeff(coeff(Fi20,D[2](f)(x0,y 0)^2),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3eG/#\"\"\" \"\"',&&%\"bG6#F'F'*&&F+6#\"\"#F')&%\"aG6$F0F0F0F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "solve(\{cond1a,cond2a,cond2b,cond3a,cond3 b,cond3c,cond3d,cond3e\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 270 93 "Ni siquiera es posible igualar simult\341neamente cond3a y cond3d , p or ejemplo, si se acepta" }}{PARA 0 "" 0 "" {TEXT 271 6 "que " } {XPPEDIT 18 0 "c[2]" "6#&%\"cG6#\"\"#" }{TEXT 272 5 " = " }{XPPEDIT 18 0 "a[22]" "6#&%\"aG6#\"#A" }{TEXT 273 45 " , como se desprende de \+ cond2a y cond2b " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "sol ve(\{c[2]=a[2,2],cond3a,cond3d\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 264 2 "b)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "solucion1:=sub s(b[2]=1,solucion) union \{b[2]=1\};" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%*solucion1G<&/&%\"bG6#\"\"\"\"\"!/&F(6#\"\"#F*/&%\"cGF.#F*F//&%\"a G6$F/F/F3" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 275 43 "La soluci\363n obte nida corresponde al tablero" }}{PARA 4 "" 0 "" {TEXT 276 19 " 1 \+ | 1" }}{PARA 4 "" 0 "" {TEXT 277 5 " " }{XPPEDIT 18 0 "1/2 " "6#*&\"\"\"F$\"\"#!\"\"" }{TEXT 280 19 " | 0 " } {XPPEDIT 18 0 "1/2" "6#*&\"\"\"F$\"\"#!\"\"" }}{PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 278 24 "------------------------" }}{PARA 4 "" 0 "" {TEXT 279 30 " | 0 1 " }}{PARA 0 "" 0 "" {TEXT 281 72 "que no hace intervenir la primera etapa y que coinc ide, por lo tanto con" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 4 "" 0 "" {TEXT 282 5 " " }{XPPEDIT 18 0 "1/2" "6#*&\"\" \"F$\"\"#!\"\"" }{TEXT 285 10 " | " }{XPPEDIT 18 0 "1/2" "6#*& \"\"\"F$\"\"#!\"\"" }}{PARA 4 "" 0 "" {TEXT -1 12 " ---------" } {TEXT 283 24 "------------------------" }}{PARA 4 "" 0 "" {TEXT 284 21 " | 1 " }}{PARA 0 "" 0 "" {TEXT 286 44 "que no es s ino el m\351todo de Gauss de 1 etapa" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 274 2 "c)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 268 23 "funci\363n de estab ilidad " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=(x,y)->lambda *y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"xG%\"yG6\"6$%)oper atorG%&arrowGF)*&%'lambdaG\"\"\"9%F/F)F)F)" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 36 "ka1:=unapply(f(x0+h,y0+h*kp1(h)),h);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%$ka1Gf*6#%\"hG6\"6$%)operatorG%&arrowGF(*&%'la mbdaG\"\"\",&%#y0GF.*&9$F.-%$kp1G6#F2F.F.F.F(F(F(" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 48 "ka2:=unapply(f(x0+c[2]*h,y0+a[2,2]*h*kp2(h)) ,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ka2Gf*6#%\"hG6\"6$%)operato rG%&arrowGF(*&%'lambdaG\"\"\",&%#y0GF.*(&%\"aG6$\"\"#F5F.9$F.-%$kp2G6# F6F.F.F.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "test:=sol ve(\{k1=subs(kp1(h)=k1,ka1(h)),k2=subs(kp2(h)=k2,ka2(h))\},\{k1,k2\}); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%testG<$/%#k2G,$*(%'lambdaG\"\" \"%#y0GF+,&F+!\"\"*(F*F+&%\"aG6$\"\"#F3F+%\"hGF+F+F.F./%#k1G,$*(F*F+F, F+,&F+F.*&F*F+F4F+F+F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "k1:=subs(test,k1);k2:=subs(test,k2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k1G,$*(%'lambdaG\"\"\"%#y0GF(,&F(!\"\"*&F'F(%\"hGF(F(F+F+" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k2G,$*(%'lambdaG\"\"\"%#y0GF(,&F(! \"\"*(F'F(&%\"aG6$\"\"#F0F(%\"hGF(F(F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "y1:=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)F'F'F/F/*,F)F'&F+6#\"\"#F'F-F'F&F',&F'F/*(F-F'&%\" aG6$F4F4F'F)F'F'F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "y1: =collect(subs(lambda=z/h,y1),y0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %#y1G*&,(\"\"\"F'*(&%\"bG6#F'F'%\"zGF',&F'!\"\"F,F'F.F.*(&F*6#\"\"#F'F ,F',&F'F.*&F,F'&%\"aG6$F2F2F'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$%)operatorG%&arrow GF(,$*(,(\"\"\"!\"\"*&,(&%\"aG6$\"\"#F6F0*&&%\"bG6#F/F/F3F/F/&F96#F6F/ F/)9$F6F/F/*&,*F3F/F/F/F8F0F;F0F/F>F/F/F/,&F/F0F>F/F0,&F/F0*&F>F/F3F/F /F0F0F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 298 64 "que es la funci \363n de estabilidad de la familia general propuesta" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "r2:=unapply(simplify(subs(solucion,r(z))) ,z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#r2Gf*6#%\"zG6\"6$%)operator G%&arrowGF(,$*(,**&\"\"#\"\"\"&%\"bG6#F0F1!\"\"*&F2F1)9$F0F1F1F8F5*(F0 F1F2F1F8F1F1F1,&F1F5F8F1F5,(*&F0F1F2F1F5F8F5*(F0F1F2F1F8F1F1F5F5F(F(F( " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 288 60 "que es la funci\363n de esta bilidad para los m\351todos de orden 2" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 287 2 "d)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 289 79 "Para el m\351 todo de GAUSS de 1 etapa, obtenido en el conjunto-solucion solucion1 " }}{PARA 0 "" 0 "" {TEXT 290 35 "tenemos como funci\363n de estabilid ad" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "rg:=unapply(simplify( subs(solucion1,r(z))),z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#rgGf*6 #%\"zG6\"6$%)operatorG%&arrowGF(,$*&,&9$\"\"\"\"\"#F0F0,&F1!\"\"F/F0F3 F3F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 291 50 "El dominio de estabi lidad, compuesto por los z = " }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT 292 35 " h tales que el m\363dulo de r1(z) " }}{PARA 0 "" 0 "" {TEXT 293 88 "sea inferior a 1 , estar\341 formado por los valores de z que disten menos del punto -2" }}{PARA 0 "" 0 "" {TEXT 294 86 "que del punto 2 . Esto corresponde al semiplano de parte real neg ativa, por lo que el" }}{PARA 0 "" 0 "" {TEXT 295 30 "m\351todo estudi ado es 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 }