{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 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 1 18 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 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 1 24 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 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 18 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 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 276 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 277 "" 1 18 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 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 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 287 "" 1 14 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 }{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 Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 263 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 264 48 "(3) Ecuaciones escalares: m\351todos de RUNGE- KUTTA" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 262 56 "Ejercicio 03-09 (del EXAMEN EXTRAORDINARIO de 22JUN11)" }}{PARA 4 " " 0 "" {TEXT -1 85 "\nConsid\351rese la familia de m\351todos de Runge -Kutta de 3 etapas y expl\355citos de tablero" }}{PARA 4 "" 0 "" {TEXT 280 13 " 0 | " }}{PARA 4 "" 0 "" {TEXT 281 7 " " } {XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT 285 8 " | " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }}{PARA 4 "" 0 "" {TEXT 284 7 " " } {XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT 286 18 " | 0 \+ " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }}{PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 282 25 "-------------------------" }}{PARA 4 "" 0 "" {TEXT 283 18 " | " }{XPPEDIT 18 0 "beta;" "6#%%bet aG" }{TEXT 287 9 " " }{XPPEDIT 18 0 "theta;" "6#%&thetaG" } {TEXT 288 9 " " }{XPPEDIT 18 0 "theta;" "6#%&thetaG" }}{PARA 4 "" 0 "" {TEXT -1 66 "De entre ellos se buscaran los que proporcionen el orden mas alto." }}{PARA 0 "" 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 72 "D\355gase cu\341l es la funci\363n de estabilidad de esos m\351todos de mayor o rden." }}}{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));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G-%\"fG6$%\"xG-%\"yG6#F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "y2:=subs(diff(y(x),x)=y1,diff(y1,x) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y2G,&--&%\"DG6#\"\"\"6#%\"fG6 $%\"xG-%\"yG6#F/F+*&--&F)6#\"\"#F,F.F+-F-F.F+F+" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 37 "y3:=subs(diff(y(x),x)=y1,diff(y2,x));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y3G,*--&%\"DG6$\"\"\"F+6#%\"fG6$%\" xG-%\"yG6#F/F+*&--&F)6$F+\"\"#F,F.F+-F-F.F+F+*&,&F4F+*&--&F)6$F8F8F,F. F+F9F+F+F+F9F+F+*&--&F)6#F8F,F.F+,&--&F)6#F+F,F.F+*&FBF+F9F+F+F+F+" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y1:=subs(\{y(x)=y0,x=x0\},y 1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Y1G-%\"fG6$%#x0G%#y0G" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y2:=subs(\{y(x)=y0,x=x0\},y2 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Y2G,&--&%\"DG6#\"\"\"6#%\"fG6 $%#x0G%#y0GF+*&--&F)6#\"\"#F,F.F+-F-F.F+F+" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 28 "Y3:=subs(\{y(x)=y0,x=x0\},y3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Y3G,*--&%\"DG6$\"\"\"F+6#%\"fG6$%#x0G%#y0GF+*&--&F)6 $F+\"\"#F,F.F+-F-F.F+F+*&,&F2F+*&--&F)6$F6F6F,F.F+F7F+F+F+F7F+F+*&--&F )6#F6F,F.F+,&--&F)6#F+F,F.F+*&F@F+F7F+F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "k1_:=f(x0,y0);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%$k1_G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "k2_:=f(x0+alpha*h,y0+alpha*h*k1_);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k2_G-%\"fG6$,&%#x0G\"\"\"*&%&alphaGF*%\"hGF*F*,&%#y0GF**(F,F* F-F*-F&6$F)F/F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "k3_:=f (x0+alpha*h,y0+alpha*h*k2_);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k3_ G-%\"fG6$,&%#x0G\"\"\"*&%&alphaGF*%\"hGF*F*,&%#y0GF**(F,F*F-F*-F&6$F(, &F/F**(F,F*F-F*-F&6$F)F/F*F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k1_0:=subs(h=0,k1_);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k1_0G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k2_0:=subs(h=0,k2_);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k2_0G -%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k3_0: =subs(h=0,k3_);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k3_0G-%\"fG6$%#x 0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k11:=diff(k1_,h) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k11G\"\"!" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 17 "k21:=diff(k2_,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k21G,&*&--&%\"DG6#\"\"\"6#%\"fG6$,&%#x0GF,*&%&alphaG F,%\"hGF,F,,&%#y0GF,*(F3F,F4F,-F.6$F1F6F,F,F,F3F,F,*(--&F*6#\"\"#F-F/F ,F3F,F8F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k31:=diff(k3 _,h);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$k31G,&*&--&%\"DG6#\"\"\"6# %\"fG6$,&%#x0GF,*&%&alphaGF,%\"hGF,F,,&%#y0GF,*(F3F,F4F,-F.6$F0,&F6F,* (F3F,F4F,-F.6$F1F6F,F,F,F,F,F3F,F,*&--&F*6#\"\"#F-F/F,,&*&F3F,F8F,F,*( F3F,F4F,,&*&-F(F9F,F3F,F,*(-F@F9F,F3F,F " 0 "" {MPLTEXT 1 0 20 "k110:=subs(h=0,k11);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k110G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k210:=subs(h=0,k21);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k210G ,&*&--&%\"DG6#\"\"\"6#%\"fG6$%#x0G%#y0GF,%&alphaGF,F,*(--&F*6#\"\"#F-F /F,F2F,-F.F/F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k310:=s ubs(h=0,k31);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k310G,&*&--&%\"DG6 #\"\"\"6#%\"fG6$%#x0G%#y0GF,%&alphaGF,F,*(--&F*6#\"\"#F-F/F,F2F,-F.F/F ,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k12:=diff(k11,h);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k12G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k22:=diff(k21,h);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$k22G,&*&,&*&--&%\"DG6$\"\"\"F.6#%\"fG6$,&%#x0GF.*&%&alphaGF.% \"hGF.F.,&%#y0GF.*(F5F.F6F.-F06$F3F8F.F.F.F5F.F.*(--&F,6$F.\"\"#F/F1F. F5F.F:F.F.F.F5F.F.*(,&*&F=F.F5F.F.*(--&F,6$FAFAF/F1F.F5F.F:F.F.F.F5F.F :F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k32:=diff(k31,h); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$k32G,(*&,&*&--&%\"DG6$\"\"\"F.6 #%\"fG6$,&%#x0GF.*&%&alphaGF.%\"hGF.F.,&%#y0GF.*(F5F.F6F.-F06$F2,&F8F. *(F5F.F6F.-F06$F3F8F.F.F.F.F.F5F.F.*&--&F,6$F.\"\"#F/F1F.,&*&F5F.F:F.F .*(F5F.F6F.,&*&--&F,6#F.F/F;F.F5F.F.*(--&F,6#FEF/F;F.F5F.F>F.F.F.F.F.F .F.F5F.F.*&,&*&FAF.F5F.F.*&--&F,6$FEFEF/F1F.FFF.F.F.FFF.F.*&-FQF1F.,&* (FEF.F5F.FIF.F.*(F5F.F6F.,&*&,&*&-F*F;F.F5F.F.*(-FBF;F.F5F.F>F.F.F.F5F .F.*(,&*&FaoF.F5F.F.*(-FYF;F.F5F.F>F.F.F.F5F.F>F.F.F.F.F.F." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k120:=subs(h=0,k12);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k120G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k220:=subs(h=0,k22);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k220G,&*&,&*&--&%\"DG6$\"\"\"F.6#%\"fG6$%#x0G%#y0GF. %&alphaGF.F.*(--&F,6$F.\"\"#F/F1F.F4F.-F0F1F.F.F.F4F.F.*(,&*&F6F.F4F.F .*(--&F,6$F:F:F/F1F.F4F.F;F.F.F.F4F.F;F.F." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 20 "k320:=subs(h=0,k32);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%k320G,(*&,&*&--&%\"DG6$\"\"\"F.6#%\"fG6$%#x0G%#y0GF.%&alphaGF .F.*(--&F,6$F.\"\"#F/F1F.F4F.-F0F1F.F.F.F4F.F.*(,&*&F6F.F4F.F.*(--&F,6 $F:F:F/F1F.F4F.F;F.F.F.F4F.F;F.F.**F:F.--&F,6#F:F/F1F.F4F.,&*&--&F,6#F .F/F1F.F4F.F.*(FEF.F4F.F;F.F.F.F." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 2 "a)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 27 "condiciones para el orden 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "Fi_0:=expand(be ta*k1_0+theta*k2_0+theta*k3_0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%% Fi_0G,&*&%%betaG\"\"\"-%\"fG6$%#x0G%#y0GF(F(*(\"\"#F(%&thetaGF(F)F(F( " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "cond1a:=coeff(Y1,f(x0,y 0))=coeff(Fi_0,f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond1a G/\"\"\",&%%betaGF&*&\"\"#F&%&thetaGF&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 27 "condiciones para el orden 2" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 46 "Fi10:=expand(beta*k110+theta*k210+theta*k310);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi10G,&**\"\"#\"\"\"%&thetaGF(--&% \"DG6#F(6#%\"fG6$%#x0G%#y0GF(%&alphaGF(F(*,F'F(F)F(--&F-6#F'F/F1F(F4F( -F0F1F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "cond2a:=(1/2)* coeff(Y2,D[1](f)(x0,y0))=coeff(Fi10,D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2aG/#\"\"\"\"\"#,$*(F(F'%&thetaGF'%&alphaGF'F '" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "cond2b:=(1/2)*coeff(co eff(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/#\"\"\"\"\"#,$*(F (F'%&thetaGF'%&alphaGF'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "sol1:=solve(\{cond1a,cond2a,cond2b\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%sol1G<%/%%betaG,&\"\"\"F)*&\"\"#F)%&thetaGF)!\"\"/%& alphaG,$*&F)F)*&\"\"%F)F,F)F-F)/F,F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 2 "b)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 258 28 "condiciones para el orden 3 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "Fi20:=expand(b eta*k120+theta*k220+theta*k320);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% %Fi20G,,**\"\"#\"\"\"%&thetaGF(--&%\"DG6$F(F(6#%\"fG6$%#x0G%#y0GF()%&a lphaGF'F(F(*,\"\"%F(F)F(--&F-6$F(F'F/F1F(F4F(-F0F1F(F(*,F'F(F)F(F4F()F " 0 "" {MPLTEXT 1 0 76 "cond3a:=(1/6)*coeff(Y3,D[1,1](f)(x0,y0))=(1/2)*coeff(Fi20,D[1,1](f )(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3aG/#\"\"\"\"\"'* &%&thetaGF')%&alphaG\"\"#F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "cond3b:=(1/6)*coeff(coeff(Y3,D[1,2](f)(x0,y0)),f(x0,y0))=(1/2)*co eff(coeff(Fi20,D[1,2](f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3bG/#\"\"\"\"\"$,$*(\"\"#F'%&thetaGF')%&alphaGF+ F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "cond3c:=(1/6)*coef f(coeff(Y3,D[2,2](f)(x0,y0)),f(x0,y0)^2)=(1/2)*coeff(coeff(Fi20,D[2,2] (f)(x0,y0)),f(x0,y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3cG /#\"\"\"\"\"'*&%&thetaGF')%&alphaG\"\"#F'" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 116 "cond3d:=(1/6)*coeff(coeff(Y3,D[2](f)(x0,y0)),D[1]( f)(x0,y0))=(1/2)*coeff(coeff(Fi20,D[2](f)(x0,y0)),D[1](f)(x0,y0));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3dG/#\"\"\"\"\"'*&%&thetaGF')%& alphaG\"\"#F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "cond3e:=( 1/6)*coeff(coeff(Y3,D[2](f)(x0,y0)^2),f(x0,y0))=(1/2)*coeff(coeff(Fi20 ,D[2](f)(x0,y0)^2),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'co nd3eG/#\"\"\"\"\"'*&%&thetaGF')%&alphaG\"\"#F'" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 90 "sol2:=solve(\{cond1a,cond2a,cond2b,cond3a,cond 3b,cond3c,cond3d,cond3e\},\{alpha,beta,theta\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%sol2G<%/%&alphaG#\"\"#\"\"$/%&thetaG#F*\"\")/%%betaG #\"\"\"\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 266 31 "metodo de mayor orden, orden 3," }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 268 12 " 0 | " }}{PARA 4 "" 0 "" {TEXT 269 18 " 2/3 | 2/3" }}{PARA 4 " " 0 "" {TEXT 272 27 " 2/3 | 0 2/3" }}{PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 270 21 "---------------------" }} {PARA 4 "" 0 "" {TEXT 271 36 " | 1/4 3/8 3/8" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 267 45 "que suel e llamarse de NYSTR\326M de tercer orden" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 261 55 "es sabido que los m\351todos de 3 etapas y orden maximo 3" }}{PARA 0 "" 0 "" {TEXT 273 29 "tienen funci\363n de estabilidad" }}{PARA 0 "" 0 "" {TEXT 274 18 " r(z) = 1 + z + " }{XPPEDIT 18 0 "1/ 2;" "6#*&\"\"\"F$\"\"#!\"\"" }{TEXT 275 1 " " }{XPPEDIT 18 0 "z^2;" "6 #*$%\"zG\"\"#" }{TEXT 276 3 " + " }{XPPEDIT 18 0 "1/6;" "6#*&\"\"\"F$ \"\"'!\"\"" }{TEXT 277 2 " " }{XPPEDIT 18 0 "z^3;" "6#*$%\"zG\"\"$" } {TEXT 278 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 265 52 "o, sea, cuatro primeros t\351rminos del desarrollo de " }{XPPEDIT 18 0 "e^z; " "6#)%\"eG%\"zG" }{TEXT 279 1 " " }}}}{MARK "0 0 0" 7 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }