{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 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 1 24 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 18 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 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 270 "" 1 18 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 18 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 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 279 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 280 "" 1 18 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 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 283 "" 1 18 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 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 286 "" 1 18 0 0 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 }{PSTYLE "Maple P lot" -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 14 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 "Normal" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 18 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 }} {SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 262 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 263 22 "(8) Estabilidad lineal" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 264 56 "Ejercicio 08-29 (del E XAMEN EXTRAORDINARIO de 07JUL12)" }{TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 67 "\nPara la familia de m\351todos impl\355citos de RUNGE-KU TTA de dos etapas" }}{PARA 4 "" 0 "" {TEXT -1 11 "de tablero " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 259 6 " " } {XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT 276 9 " | " } {XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT 277 9 " 0" }}{PARA 4 "" 0 "" {TEXT 260 6 " " }{XPPEDIT 18 0 "2/3;" "6#*&\"\"#\"\"\" \"\"$!\"\"" }{TEXT 266 9 " | " }{XPPEDIT 18 0 "1/3;" "6#*&\"\"\" F$\"\"$!\"\"" }{TEXT 265 8 " " }{XPPEDIT 18 0 "1/3;" "6#*&\"\" \"F$\"\"$!\"\"" }}{PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 256 17 "-----------------" }}{PARA 4 "" 0 "" {TEXT 257 17 " \+ | " }{XPPEDIT 18 0 "1/4;" "6#*&\"\"\"F$\"\"%!\"\"" }{TEXT 258 9 " \+ " }{XPPEDIT 18 0 "3/4;" "6#*&\"\"$\"\"\"\"\"%!\"\"" }{TEXT 261 4 " " }}{PARA 4 "" 0 "" {TEXT -1 66 "calc\372lese el orden m \341ximo de consistencia y d\355gase si los casos de" }}{PARA 4 "" 0 " " {TEXT -1 54 "orden m\341ximo son o no A-estables. Para el m\351todo \+ con " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT -1 8 " = 2/3 ," }} {PARA 4 "" 0 "" {TEXT -1 45 "d\355gase qu\351 orden posee y si es o no 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:=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 49 "k1_:=unapply(f(x0+alpha*h,y0+alpha*h*kp1_(h)), h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "k2_:=unapply(f(x0+2/ 3*h,y0+1/3*h*kp1_(h)+1/3*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 "k1 1:=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,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,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 267 27 "condiciones para el orden 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "Fi_0:=e xpand((1/4)*k1_0+(3/4)*k2_0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi _0G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "co nd1a:=coeff(Y1,f(x0,y0))=coeff(Fi_0,f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond1aG/\"\"\"F&" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 25 "El orden es de 1 al menos" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 268 27 "condiciones para el orden 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "Fi10:=expand((1/4)*k110+(3/4)*k210);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi10G,**&#\"\"\"\"\"%F(*&--&%\"DG6# F(6#%\"fG6$%#x0G%#y0GF(%&alphaGF(F(F(*&F'F(*(--&F.6#\"\"#F0F2F(F5F(-F1 F2F(F(F(*&#F(F " 0 "" {MPLTEXT 1 0 66 "cond2a:=(1/2)*coeff(Y2,D[1](f)(x0,y0))=coeff(Fi10, D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2aG/#\"\"\" \"\"#,&*&\"\"%!\"\"%&alphaGF'F'F&F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "cond2b:=(1/2)*coeff(coeff(Y2,D[2](f)(x0,y0)),f(x0,y0) )=coeff(coeff(Fi10,D[2](f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2bG/#\"\"\"\"\"#,&*&\"\"%!\"\"%&alphaGF'F'F&F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "orden2:=solve(\{cond2a,co nd2b\},alpha);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'orden2G<#/%&alpha G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "alpha:=subs(orden 2,alpha);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&alphaG\"\"!" }}} {EXCHG {PARA 256 "" 0 "" {TEXT -1 32 "El orden es de 2 al menos para \+ " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT -1 4 " = 0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 269 28 "condiciones para el orden 3 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "Fi20:=expand((1/4)*k120+(3/4)*k220) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi20G,,*&#\"\"\"\"\"$F(--&%\"D G6$F(F(6#%\"fG6$%#x0G%#y0GF(F(*&#\"\"#F)F(*&--&F-6$F(F6F/F1F(-F0F1F(F( F(*&F'F(*&--&F-6$F6F6F/F1F()F " 0 "" {MPLTEXT 1 0 70 "cond3a:=(1/3)*coeff(Y3,D[1,1](f)(x0,y0))=coeff(Fi20,D [1,1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3aG/#\"\" \"\"\"$F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "cond3b:=(1/3) *coeff(coeff(Y3,D[1,2](f)(x0,y0)),f(x0,y0))=coeff(coeff(Fi20,D[1,2](f) (x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3bG/#\" \"#\"\"$F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "cond3c:=(1/3 )*coeff(coeff(Y3,D[2,2](f)(x0,y0)),f(x0,y0)^2)=coeff(coeff(Fi20,D[2,2] (f)(x0,y0)),f(x0,y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3cG /#\"\"\"\"\"$F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "cond3d: =(1/3)*coeff(coeff(Y3,D[2](f)(x0,y0)),D[1](f)(x0,y0))=coeff(coeff(Fi20 ,D[2](f)(x0,y0)),D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %'cond3dG/#\"\"\"\"\"$F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "cond3e:=(1/3)*coeff(coeff(Y3,D[2](f)(x0,y0)^2),f(x0,y0))=coeff(co eff(Fi20,D[2](f)(x0,y0)^2),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3eG/#\"\"\"\"\"$F&" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 32 "El orden es de 3 al menos para " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG " }{TEXT -1 3 " =0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 272 8 "orden 4 " } }}{EXCHG {PARA 0 "" 0 "" {TEXT 271 15 "El m\351todo con " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT -1 3 " =0" }{TEXT 275 41 " no es el m\351todo de GAUSS de dos etapas." }}{PARA 0 "" 0 "" {TEXT 273 39 "Po r lo tanto, no se alcanza el orden 4 " }}{PARA 0 "" 0 "" {TEXT 274 41 "O sea, el orden maximo de la familia es 3" }{TEXT -1 7 " para " } {XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT -1 3 " =0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 285 29 "funci\363n de estabilidad para " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT 286 8 " genaral" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface(labeling=false):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=(x,y)->lambda*y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"xG%\"yG6\"6$%)operatorG%&arrowGF)*&%'lambdaG\"\"\"9 %F/F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "ka1:=unapply(f (x0+alpha*h,y0+alpha*h*kp1(h)),h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%$ka1Gf*6#%\"hG6\"6$%)operatorG%&arrowGF(*&%'lambdaG\"\"\",&%#y0GF.*( %&alphaGF.9$F.-%$kp1G6#F3F.F.F.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "test:=solve(\{k1=subs(kp1(h)=k1,ka1(h))\},k1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%testG<#/%#k1G,$*(%'lambdaG\"\"\"%#y 0GF+,&F+!\"\"*(F*F+%&alphaGF+%\"hGF+F+F.F." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 18 "k1:=subs(test,k1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k1G,$*(%'lambdaG\"\"\"%#y0GF(,&F(!\"\"*(F'F(%&alphaGF(%\"hGF(F(F +F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "ka2:=unapply(f(x0+(2 /3)*h,y0+(1/3)*h*k1+(1/3)*h*kp2(h)),h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ka2Gf*6#%\"hG6\"6$%)operatorG%&arrowGF(*&%'lambdaG\"\"\",(%#y 0GF.*&#F.\"\"$F.**9$F.F-F.F0F.,&F.!\"\"*(F-F.%&alphaGF.F5F.F.F7F.F7*&# F.F3F.*&F5F.-%$kp2G6#F5F.F.F.F.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "test:=solve(\{k2=subs(kp2(h)=k2,ka2(h))\},k2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%testG<#/%#k2G,$*,%'lambdaG\"\"\"%#y 0GF+,(\"\"$!\"\"**F.F+F*F+%&alphaGF+%\"hGF+F+*&F*F+F2F+F/F+,&F+F/*(F*F +F1F+F2F+F+F/,&F.F/F3F+F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "k2:=subs(test,k2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k2G,$*,%' lambdaG\"\"\"%#y0GF(,(\"\"$!\"\"**F+F(F'F(%&alphaGF(%\"hGF(F(*&F'F(F/F (F,F(,&F(F,*(F'F(F.F(F/F(F(F,,&F+F,F0F(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'%'lambdaG F'F&F',&F'F**(F,F'%&alphaGF'F+F'F'F*F**0\"\"*F'F)F*F+F'F,F'F&F'F-F*,& \"\"$F**&F,F'F+F'F'F*F'*2F1F'F)F*F,\"\"#F&F'F-F*F2F*F/F'F+F6F**0F3F'F) F*F,F6F&F'F-F*F2F*F+F6F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "y1:=collect(subs(lambda=z/h,y1),y0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G*&,,\"\"\"F'*(\"\"%!\"\"%\"zGF',&F'F**&F+F'%&alphaGF'F'F*F**, \"\"*F'F)F*F+F'F,F*,&\"\"$F*F+F'F*F'*.F0F'F)F*F+\"\"#F,F*F1F*F.F'F**,F 2F'F)F*F+F4F,F*F1F*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/*(,(\"#7!\"\"*&,&*&\"\"&F/%&alphaGF/F/\"\"#F4F/)9$F:F/F/*&,&\"\") F4*&F3F/F9F/F/F/F " 0 "" {MPLTEXT 1 0 8 "restart:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "alpha:=0;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%&alphaG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface(labeling=false):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=(x,y)->lambda*y;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%\"fGf*6$%\"xG%\"yG6\"6$%)operatorG%&arrowGF)*&%'lambdaG\"\"\"9%F/F )F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "ka1:=unapply(f(x0+ alpha*h,y0+alpha*h*kp1(h)),h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k a1Gf*6#%\"hG6\"6$%)operatorG%&arrowGF(*&%'lambdaG\"\"\"%#y0GF.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "test:=solve(\{k1=subs(kp1 (h)=k1,ka1(h))\},k1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%testG<#/%# k1G*&%'lambdaG\"\"\"%#y0GF*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "k1:=subs(test,k1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k1G*&%'la mbdaG\"\"\"%#y0GF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "ka2:= unapply(f(x0+(2/3)*h,y0+(1/3)*h*k1+(1/3)*h*kp2(h)),h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ka2Gf*6#%\"hG6\"6$%)operatorG%&arrowGF(*&%'lamb daG\"\"\",(%#y0GF.*&#F.\"\"$F.*(9$F.F-F.F0F.F.F.*&F2F.*&F5F.-%$kp2G6#F 5F.F.F.F.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "test:=so lve(\{k2=subs(kp2(h)=k2,ka2(h))\},k2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%testG<#/%#k2G,$**%'lambdaG\"\"\"%#y0GF+,&\"\"$F+*&F*F+%\"hGF+ F+F+,&F.!\"\"F/F+F2F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "k2 :=subs(test,k2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k2G,$**%'lambda G\"\"\"%#y0GF(,&\"\"$F(*&F'F(%\"hGF(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\"\"\"**\"\"%!\"\"% \"hGF'%'lambdaGF'F&F'F'*.\"\"*F'F)F*F+F'F,F'F&F',&\"\"$F**&F,F'F+F'F'F *F**.F0F'F)F*F,\"\"#F&F'F/F*F+F3F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "y1:=collect(subs(lambda=z/h,y1),y0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G*&,*\"\"\"F'*&\"\"%!\"\"%\"zGF'F'**\"\"*F'F) F*F+F',&\"\"$F*F+F'F*F***F/F'F)F*F+\"\"#F.F*F*F'%#y0GF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "r:=unapply(collect(simplify(y1/y0), z),z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rGf*6#%\"zG6\"6$%)operat orG%&arrowGF(,$*&#\"\"\"\"\"#F/*&,(\"\"'F/*&\"\"%F/9$F/F/*$)F6F0F/F/F/ ,&\"\"$!\"\"F6F/F;F/F;F(F(F(" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 281 26 " Lo que hace que el m\351todo " }{TEXT 282 6 "para " }{XPPEDIT 18 0 "a lpha;" "6#%&alphaG" }{TEXT 283 20 " = 0 (orden maximo) " }{TEXT 284 21 "no sea A-estable. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 270 29 "fun ci\363n de estabilidad para " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" } {TEXT 278 6 " = 2/3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "resta rt:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "alpha:=2/3;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&alphaG#\"\"#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface(labeling=false):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=(x,y)->lambda*y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"xG%\"yG6\"6$%)operatorG%&arrowGF)*&%' lambdaG\"\"\"9%F/F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 " ka1:=unapply(f(x0+alpha*h,y0+alpha*h*kp1(h)),h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ka1Gf*6#%\"hG6\"6$%)operatorG%&arrowGF(*&%'lambdaG\" \"\",&%#y0GF.*&#\"\"#\"\"$F.*&9$F.-%$kp1G6#F6F.F.F.F.F(F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "test:=solve(\{k1=subs(kp1(h) =k1,ka1(h))\},k1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%testG<#/%#k1G 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