{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE " " 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 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 }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 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 1 "#" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 31 "# inicio del fichero RKUT22.MWS" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 1 "#" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 45 "# modelo para \+ estudiar metodos de Runge-Kutta" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 45 "# de dos evaluaciones k1 y k2 y orden 2 para " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 57 "# ecuaciones escalares aut\363nomas (EA), no aut\363 nomas (EN) " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 53 "# y para sistemas aut \363nomos (SA) y no aut\363nomos (SN)." }}{PARA 0 "" 0 "" {MPLTEXT 0 21 37 "# Empezaremos con metodos explicitos." }}{PARA 0 "" 0 "" {MPLTEXT 0 21 1 "#" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 36 "# Empezamos co n una ecuaci\363n escalar" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 28 "# \+ yp = f(x,y) , y(a) = " }{XPPEDIT 18 0 "alpha" "I&alphaG6\"" }{MPLTEXT 0 21 2 " " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 8 "# o bien" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 26 "# yp = f(y) , y(a) = " }{XPPEDIT 18 0 "alp ha" "I&alphaG6\"" }{MPLTEXT 0 21 15 " " }}{PARA 0 "" 0 " " {MPLTEXT 0 21 23 "# en el caso aut\363nomo. " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 16 "# El m\351todo es " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 19 "# k1:=f(x0,y0)" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 38 "# \+ k2:=f(x0+c[2]*h,y0+a[2,1]*h*k1)" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 14 " # y finalmente" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 33 "# y1:=y0+h*(b [1]*k1+b[2]*k2)" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 28 "# o sea Fi0 que r epresenta " }{XPPEDIT 18 0 "Phi(h)" "-%$PhiG6#%\"hG" }{MPLTEXT 0 21 3 " = " }{XPPEDIT 18 0 "Phi(x0,y0,h)" "-%$PhiG6%%#x0G%#y0G%\"hG" } {MPLTEXT 0 21 4 " es" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 36 "# Fi0: =b[1]*k1+b[2]*k2+b[3]*k3 " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 28 "# y Fi1 es su derivada, " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 54 "# mientras \+ que, por la parte de la verdadera soluci\363n," }}{PARA 0 "" 0 "" {MPLTEXT 0 21 22 "# fk que representa " }{XPPEDIT 18 0 "f^([k])" ")% \"fG7#%\"kG" }{MPLTEXT 0 21 14 " (x0,y0) vale" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 57 "# f(k+1):=diff(fk,x):=D[1](fk)+f0*D[2](fk) \+ " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 58 "# Para las condiciones de o rden, lo que se hace es imponer" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 16 "# sucesivamente " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 16 "# Fik(0) = \+ " }{XPPEDIT 18 0 "1/(k+1)" "*&\"\"\"F#,&%\"kGF#F#F#!\"\"" }{MPLTEXT 0 21 4 " fk " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 25 "# en este caso para k= 0,1" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 43 "# Para el t\351rmino del erro r se calculan los" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 40 "# distintos coe ficientes que aparecen en" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 7 "# \+ " }{XPPEDIT 18 0 "1/(2!)" "*&\"\"\"F#-%*factorialG6#\"\"#!\"\"" } {MPLTEXT 0 21 10 " Fi2(0) - " }{XPPEDIT 18 0 "1/(3!)" "*&\"\"\"F#-%*fa ctorialG6#\"\"$!\"\"" }{MPLTEXT 0 21 19 " f2 " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 28 "# para el orden 2 del m\351todo" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 1 "#" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 40 "# Pa ra sistemas aut\363nomos y no aut\363nomos" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 45 "# todo es similar, pero ahora las condiciones" }} {PARA 0 "" 0 "" {MPLTEXT 0 21 19 "# Fik(0)[i] = " }{XPPEDIT 18 0 "1/(k+1)" "*&\"\"\"F#,&%\"kGF#F#F#!\"\"" }{MPLTEXT 0 21 37 " fk[i] \+ " }}{PARA 0 "" 0 "" {MPLTEXT 0 21 41 "# y l os coeficientes del t\351rmino de error" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 57 "# se imponen s\363lo sobre la primera componente i=1, ya que" } }{PARA 0 "" 0 "" {MPLTEXT 0 21 26 "# las otras son id\351nticas " }} {PARA 0 "" 0 "" {MPLTEXT 0 21 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 35 "# PARA ECUACIONES NO AUTONOMAS (EN)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 26 "interface(labeling=false):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 37 "# desarrollo de la verdadera solucion" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "y:=unapply(y(x),x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "f:=unapply(f(x,y),x,y):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f0:=f(x,y(x)):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 44 "f1:=subs(diff(y(x),x)=f(x,y(x)),diff(f0,x)): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "f2:=subs(diff(y(x),x)=f (x,y(x)),diff(f1,x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "f0 :=subs(\{y(x)=y0,x=x0\},f0):ENf0:=expand(f0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ENf0G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 45 "f1:=subs(\{y(x)=y0,x=x0\},f1):ENf1:=expand(f1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ENf1G,&--&%\"DG6#\"\"\"6#%\"fG6$%#x 0G%#y0GF+*&--&F)6#\"\"#F,F.F+-F-F.F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "f2:=subs(\{y(x)=y0,x=x0\},f2):ENf2:=expand(f2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ENf2G,,--&%\"DG6$\"\"\"F+6#%\"fG6$% #x0G%#y0GF+*&--&F)6$F+\"\"#F,F.F+-F-F.F+F6*&--&F)6$F6F6F,F.F+F7F6F+*&- -&F)6#F6F,F.F+--&F)6#F+F,F.F+F+*&F>F6F7F+F+" }}}{EXCHG {PARA 0 "" 0 " " {MPLTEXT 0 21 23 "# desarrollo del m\351todo" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 12 "k10:=f(x,y):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "k20:=f(x+c[2]*h,y+a[2,1]*h*k10):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 20 "k100:=subs(h=0,k10):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 20 "k200:=subs(h=0,k20):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "Fi0:=b[1]*k100+b[2]*k200:Fi0:=subs(\{x=x0,y=y0\} ,Fi0):ENFi0:=expand(Fi0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&ENFi0G ,&*&&%\"bG6#\"\"\"F*-%\"fG6$%#x0G%#y0GF*F**&&F(6#\"\"#F*F+F*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k11:=diff(k10,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k21:=diff(k20,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 71 "Fi1:=b[1]*k110+b[2]*k210:Fi1 :=subs(\{x=x0,y=y0\},Fi1):ENFi1:=expand(Fi1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&ENFi1G,&*(&%\"bG6#\"\"#\"\"\"--&%\"DG6#F+6#%\"fG6$%# x0G%#y0GF+&%\"cGF)F+F+**F'F+--&F/F)F1F3F+&%\"aG6$F*F+F+-F2F3F+F+" }}} {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 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 71 "Fi2:=b[1]*k120+b[2]*k220:Fi2 :=subs(\{x=x0,y=y0\},Fi2):ENFi2:=expand(Fi2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&ENFi2G,(*(&%\"bG6#\"\"#\"\"\"--&%\"DG6$F+F+6#%\"fG6$ %#x0G%#y0GF+&%\"cGF)F*F+*,F'F+F6F+--&F/6$F+F*F1F3F+&%\"aG6$F*F+F+-F2F3 F+F***F'F+F=F*F@F*--&F/6$F*F*F1F3F+F+" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 24 "# consistencia y orden 1" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 53 "ENcond1a:=coeff(ENFi0,f(x0,y0))=coeff(ENf0,f(x0,y0) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)ENcond1aG/,&&%\"bG6#\"\"\"F*& F(6#\"\"#F*F*" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# condicion es para el orden 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "ENcon d2a:=coeff(ENFi1,D[1](f)(x0,y0))=coeff((1/2)*ENf1,D[1](f)(x0,y0));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%)ENcond2aG/*&&%\"bG6#\"\"#\"\"\"&%\" cGF)F+#F+F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "ENcond2b:=c oeff(coeff(ENFi1,D[2](f)(x0,y0)),f(x0,y0))=coeff(coeff((1/2)*ENf1,D[2] (f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)ENcond2bG /*&&%\"bG6#\"\"#\"\"\"&%\"aG6$F*F+F+#F+F*" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 34 "# coeficiente del t\351rmino de error" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "ENterm:=expand((1/2!)*ENFi2-(1/3!)* ENf2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "ENerro3a:=coeff(E Nterm,D[1,1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)ENerro3 aG,&*&&%\"bG6#\"\"#\"\"\"&%\"cGF)F*#F+F*#!\"\"\"\"'F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "ENerro3b:=coeff(coeff(ENterm,D[1,2] (f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)ENerro3bG ,&*(&%\"bG6#\"\"#\"\"\"&%\"cGF)F+&%\"aG6$F*F+F+F+#!\"\"\"\"$F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "ENerro3c:=coeff(coeff(ENterm ,D[2,2](f)(x0,y0)),f(x0,y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%) ENerro3cG,&*&&%\"bG6#\"\"#\"\"\"&%\"aG6$F*F+F*#F+F*#!\"\"\"\"'F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "ENerro3d:=coeff(coeff(ENterm ,D[2](f)(x0,y0)),D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %)ENerro3dG#!\"\"\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "E Nerro3e:=coeff(coeff(ENterm,D[2](f)(x0,y0)^2),f(x0,y0));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%)ENerro3eG#!\"\"\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 28 "# soluciones para el orden 2" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 67 "ENsolve221:=solve(\{ENcond1a,ENcond2a,ENcond 2b\},\{b[1],b[2],a[2,1]\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+ENso lve221G<%/&%\"bG6#\"\"\",$*&,&!\"\"F*&%\"cG6#\"\"#F2F*F/F.#F*F2/&%\"aG 6$F2F*F//&F(F1,$*$F/F.F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "ENsolve222:=solve(\{ENcond1a,ENcond2a,ENcond2b,c[2]=0\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+ENsolve222G6\"" }}}{EXCHG {PARA 0 "" 0 " " {MPLTEXT 0 21 24 "# minimizaci\363n del error" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 141 "ENerror221:=solve(subs(ENsolve221,\{ENerro3a, ENerro3b,ENerro3c\})) union subs(solve(subs(ENsolve221,\{ENerro3a,ENer ro3b,ENerro3c\})),ENsolve221);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+E Nerror221G<&/&%\"cG6#\"\"##F*\"\"$/&%\"bG6#\"\"\"#F1\"\"%/&%\"aG6$F*F1 F+/&F/F)#F,F3" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 32 "# PARA ECUA CIONES AUTONOMAS (EA)" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 37 "# d esarrollo de la verdadera solucion" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "y:=unapply(y(x),x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=unapply(f(y),y):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "f0:=f(y(x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "f1:=subs(diff(y(x),x)=f(y(x)),diff(f0,x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "f2:=subs(diff(y(x),x)=f(y(x)),diff(f1,x)):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "f0:=subs(\{y(x)=y0,x=x0\}, f0):EAf0:=expand(f0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%EAf0G-%\"f G6#%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "f1:=subs(\{y(x) =y0,x=x0\},f1):EAf1:=expand(f1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% %EAf1G*&--%\"DG6#%\"fG6#%#y0G\"\"\"-F*F+F-" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 45 "f2:=subs(\{y(x)=y0,x=x0\},f2):EAf2:=expand(f2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%EAf2G,&*&---%#@@G6$%\"DG\"\"#6#%\"f G6#%#y0G\"\"\"-F/F0F-F2*&--F,F.F0F-F3F2F2" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 23 "# desarrollo del m\351todo" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "k10:=f(y):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k20:=f(y+a[2,1]*h*k10):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k100:=subs(h=0,k10):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k200:=subs(h=0,k20):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "Fi0:=b[1]*k100+b[2]*k200:Fi0:=subs(\{x=x0,y=y0\},Fi0) :EAFi0:=expand(Fi0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&EAFi0G,&*&& %\"bG6#\"\"\"F*-%\"fG6#%#y0GF*F**&&F(6#\"\"#F*F+F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k11:=diff(k10,h):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 17 "k21:=diff(k20,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 71 "Fi1:=b[1]*k110+b[2]*k210:Fi1:=subs(\{x=x0,y=y0\},Fi1) :EAFi1:=expand(Fi1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&EAFi1G**&% \"bG6#\"\"#\"\"\"--%\"DG6#%\"fG6#%#y0GF*&%\"aG6$F)F*F*-F/F0F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k12:=diff(k11,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k22:=diff(k21,h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k120:=subs(h=0,k12):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k220:=subs(h=0,k22):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "Fi2:=b[1]*k120+b[2]*k220:Fi2 :=subs(\{x=x0,y=y0\},Fi2):EAFi2:=expand(Fi2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&EAFi2G**&%\"bG6#\"\"#\"\"\"---%#@@G6$%\"DGF)6#%\"fG6 #%#y0GF*&%\"aG6$F)F*F)-F2F3F)" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 24 "# consistencia y orden 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "EAcond1a:=coeff(EAFi0,f(y0))=coeff(EAf0,f(y0));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%)EAcond1aG/,&&%\"bG6#\"\"\"F*&F(6#\"\"#F*F*" } }}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# condiciones para el orden 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "#EAcond2a" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "EAcond2b:=coeff(coeff(EAFi1,D(f)(y0 )),f(y0))=coeff(coeff((1/2)*EAf1,D(f)(y0)),f(y0));" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%)EAcond2bG/*&&%\"bG6#\"\"#\"\"\"&%\"aG6$F*F+F+#F+F* " }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 34 "# coeficiente del t\351r mino de error" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "EAterm:=ex pand((1/2!)*EAFi2-(1/3!)*EAf2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "#EAerro3a" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "#EAerro3 b" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "EAerro3c:=coeff(coeff( EAterm,(D@@2)(f)(y0)),f(y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%) EAerro3cG,&*&&%\"bG6#\"\"#\"\"\"&%\"aG6$F*F+F*#F+F*#!\"\"\"\"'F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "#EAerro3d" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "EAerro3e:=coeff(coeff(EAterm,D(f)(y0)^2),f( y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)EAerro3eG#!\"\"\"\"'" }}} {EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 28 "# soluciones para el orden 2 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "EAsolve221:=solve(\{EAc ond1a,EAcond2b,c2=a[2,1]\},\{b[1],b[2],a[2,1]\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+EAsolve221G<%/&%\"bG6#\"\"#,$*$%#c2G!\"\"#\"\"\"F*/& F(6#F0,$*&,&F.F0F-F*F0F-F.F//&%\"aG6$F*F0F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "EAsolve222:=solve(\{EAcond1a,EAcond2b,a[2,1]=0\}, \{b[1],b[2],a[2,1]\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+EAsolve22 2G6\"" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 24 "# minimizaci\363n d el error" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "EAerror221:=sub s(solve(subs(EAsolve221,\{EAerro3c\})),EAsolve221);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%+EAerror221G<%/&%\"bG6#\"\"\"#F*\"\"%/&%\"aG6$\"\"# F*#F1\"\"$/&F(6#F1#F3F," }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 33 "# PARA SISTEMAS NO AUTONOMOS (SN)" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 37 "# desarrollo de la verdadera solucion" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 25 "y[1]:=unapply(y[1](x),x):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 25 "y[2]:=unapply(y[2](x),x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "f[1]:=unapply(f[1](x,y[1],y[2]),x,y[1],y[ 2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "f[2]:=unapply(f[2]( x,y[1],y[2]),x,y[1],y[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "f0[1]:=f[1](x,y[1](x),y[2](x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "f0[2]:=f[2](x,y[1](x),y[2](x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "f1[1]:=subs(\{diff(y[1](x),x)=f[1](x,y[1](x) ,y[2](x)),diff(y[2](x),x)=f[2](x,y[1](x),y[2](x))\},diff(f0[1],x)):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "f1[2]:=subs(\{diff(y[1](x ),x)=f[1](x,y[1](x),y[2](x)),diff(y[2](x),x)=f[2](x,y[1](x),y[2](x))\} ,diff(f0[2],x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "f2[1]: =subs(\{diff(y[1](x),x)=f[1](x,y[1](x),y[2](x)),diff(y[2](x),x)=f[2](x ,y[1](x),y[2](x))\},diff(f1[1],x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "f2[2]:=subs(\{diff(y[1](x),x)=f[1](x,y[1](x),y[2](x) ),diff(y[2](x),x)=f[2](x,y[1](x),y[2](x))\},diff(f1[2],x)):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f0[1]:=subs(\{y[1](x)=y0[1], y[2](x)=y0[2],x=x0\},f0[1]):SNf0[1]:=expand(f0[1]);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>&%%SNf0G6#\"\"\"-&%\"fGF&6%%#x0G&%#y0GF&&F.6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f0[2]:=subs(\{y[1](x)=y0[ 1],y[2](x)=y0[2],x=x0\},f0[2]):SNf0[2]:=expand(f0[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f1[1]:=subs(\{y[1](x)=y0[1],y[2](x) =y0[2],x=x0\},f1[1]):SNf1[1]:=expand(f1[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%%SNf1G6#\"\"\",(--&%\"DGF&6#&%\"fGF&6%%#x0G&%#y0GF&& F36#\"\"#F'*&--&F,F5F-F0F'-F.F0F'F'*&--&F,6#\"\"$F-F0F'-&F/F5F0F'F'" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f1[2]:=subs(\{y[1](x)=y0[1 ],y[2](x)=y0[2],x=x0\},f1[2]):SNf1[2]:=expand(f1[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f2[1]:=subs(\{y[1](x)=y0[1],y[2](x) =y0[2],x=x0\},f2[1]):SNf2[1]:=expand(f2[1]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%%SNf2G6#\"\"\",:--&%\"DG6$F'F'6#&%\"fGF&6%%#x0G&%#y0 GF&&F46#\"\"#F'*&--&F,6$F'F7F.F1F'-F/F1F'F7*&--&F,6$F'\"\"$F.F1F'-&F0F 6F1F'F7*&--&F,6$F7F7F.F1F'F=F7F'*(F=F'--&F,6$F7FCF.F1F'FDF'F7*&--&F,F6 F.F1F'--&F,F&F.F1F'F'*&FQF7F=F'F'*(FQF'--&F,6#FCF.F1F'FDF'F'*&--&F,6$F CFCF.F1F'FDF7F'*&FYF'--FV6#FEF1F'F'*(FYF'--FSF_oF1F'F=F'F'*(FYF'--FenF _oF1F'FDF'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f2[2]:=subs (\{y[1](x)=y0[1],y[2](x)=y0[2],x=x0\},f2[2]):SNf2[2]:=expand(f2[2]):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 23 "# desarrollo del m\351todo " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k10[1]:=f[1](x,y[1],y[2 ]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k10[2]:=f[2](x,y[1], y[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "k20[1]:=f[1](x+c[ 2]*h,y[1]+a[2,1]*h*k10[1],y[2]+a[2,1]*h*k10[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "k20[2]:=f[2](x+c[2]*h,y[1]+a[2,1]*h*k10[1],y[ 2]+a[2,1]*h*k10[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k10 0[1]:=subs(h=0,k10[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 " k100[2]:=subs(h=0,k10[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k200[1]:=subs(h=0,k20[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k200[2]:=subs(h=0,k20[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "Fi0[1]:=b[1]*k100[1]+b[2]*k200[1]:Fi0[1]:=subs(\{x=x 0,y[1]=y0[1],y[2]=y0[2]\},Fi0[1]):SNFi0[1]:=expand(Fi0[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&SNFi0G6#\"\"\",&*&&%\"bGF&F'-&%\"fGF&6%% #x0G&%#y0GF&&F26#\"\"#F'F'*&&F+F4F'F,F'F'" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 109 "Fi0[2]:=b[1]*k100[2]+b[2]*k200[2]:Fi0[2]:=subs(\{x =x0,y[1]=y0[1],y[2]=y0[2]\},Fi0[2]):SNFi0[2]:=expand(Fi0[2]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k11[1]:=diff(k10[1],h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k11[2]:=diff(k10[2],h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k21[1]:=diff(k20[1],h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k21[2]:=diff(k20[2],h):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k110[1]:=subs(h=0,k11[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k110[2]:=subs(h=0,k11[2]) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k210[1]:=subs(h=0,k21[ 1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k210[2]:=subs(h=0,k 21[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "Fi1[1]:=b[1]*k1 10[1]+b[2]*k210[1]:Fi1[1]:=subs(\{x=x0,y[1]=y0[1],y[2]=y0[2]\},Fi1[1]) :SNFi1[1]:=expand(Fi1[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&SNFi 1G6#\"\"\",(*(&%\"bG6#\"\"#F'--&%\"DGF&6#&%\"fGF&6%%#x0G&%#y0GF&&F8F,F '&%\"cGF,F'F'**F*F'--&F1F,F2F5F'&%\"aG6$F-F'F'-F3F5F'F'**F*F'--&F16#\" \"$F2F5F'F@F'-&F4F,F5F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "Fi1[2]:=b[1]*k110[2]+b[2]*k210[2]:Fi1[2]:=subs(\{x=x0,y[1]=y0[1], y[2]=y0[2]\},Fi1[2]):SNFi1[2]:=expand(Fi1[2]):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 23 "k12[1]:=diff(k11[1],h):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 23 "k12[2]:=diff(k11[2],h):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 23 "k22[1]:=diff(k21[1],h):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 23 "k22[2]:=diff(k21[2],h):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 26 "k120[1]:=subs(h=0,k12[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k120[2]:=subs(h=0,k12[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k220[1]:=subs(h=0,k22[1]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k220[2]:=subs(h=0,k22[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "Fi2[1]:=b[1]*k120[1]+b[2 ]*k220[1]:Fi2[1]:=subs(\{x=x0,y[1]=y0[1],y[2]=y0[2]\},Fi2[1]):SNFi2[1] :=expand(Fi2[1]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%&SNFi2G6#\"\" \",.*(&%\"bG6#\"\"#F'--&%\"DG6$F'F'6#&%\"fGF&6%%#x0G&%#y0GF&&F9F,F'&% \"cGF,F-F'*,F*F'F;F'--&F16$F'F-F3F6F'&%\"aG6$F-F'F'-F4F6F'F-*,F*F'F;F' --&F16$F'\"\"$F3F6F'FBF'-&F5F,F6F'F-**F*F'FBF-FEF---&F16$F-F-F3F6F'F'* ,F*F'FBF-FEF'--&F16$F-FKF3F6F'FLF'F-**F*F'FBF-FLF---&F16$FKFKF3F6F'F' " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "Fi2[2]:=b[1]*k120[2]+b [2]*k220[2]:Fi2[2]:=subs(\{x=x0,y[1]=y0[1],y[2]=y0[2]\},Fi2[2]):SNFi2[ 1]:=expand(Fi2[1]):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 24 "# con sistencia y orden 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "SNco nd1a:=coeff(SNFi0[1],f[1](x0,y0[1],y0[2]))=coeff(SNf0[1],f[1](x0,y0[1] ,y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)SNcond1aG/,&&%\"bG6#\" \"\"F*&F(6#\"\"#F*F*" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# co ndiciones para el orden 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "SNcond2a:=coeff(SNFi1[1],D[1](f[1])(x0,y0[1],y0[2]))=coeff((1/2)* SNf1[1],D[1](f[1])(x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%)SNcond2aG/*&&%\"bG6#\"\"#\"\"\"&%\"cGF)F+#F+F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 158 "SNcond2b1:=coeff(coeff(SNFi1[1],D[2](f[1 ])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2]))=coeff(coeff((1/2)*SNf1[1],D[ 2](f[1])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond2b1G/*&&%\"bG6#\"\"#\"\"\"&%\"aG6$F*F+F+#F+F* " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 158 "SNcond2b2:=coeff(coeff (SNFi1[1],D[3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]))=coeff(coef f((1/2)*SNf1[1],D[3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNcond2b2G/*&&%\"bG6#\"\"#\"\"\"&% \"aG6$F*F+F+#F+F*" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 34 "# coefi ciente del t\351rmino de error" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "SNterm[1]:=expand((1/2!)*SNFi2[1]-(1/3!)*SNf2[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "SNerro3a:=coeff(SNterm[1],D[1,1](f[ 1])(x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)SNerro3aG, &*&&%\"bG6#\"\"#\"\"\"&%\"cGF)F*#F+F*#!\"\"\"\"'F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "SNerro3b1:=coeff(coeff(SNterm[1],D[1,2](f[1 ])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNerro3b1G,&*(&%\"bG6#\"\"#\"\"\"&%\"cGF)F+&%\"aG6$F *F+F+F+#!\"\"\"\"$F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "SNe rro3b2:=coeff(coeff(SNterm[1],D[1,3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0 [1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNerro3b2G,&*(&%\"b G6#\"\"#\"\"\"&%\"cGF)F+&%\"aG6$F*F+F+F+#!\"\"\"\"$F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "SNerro3c1:=coeff(coeff(SNterm[1],D[ 2,2](f[1])(x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2])^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNerro3c1G,&*&&%\"bG6#\"\"#\"\"\"&%\"aG6$F*F+F*#F +F*#!\"\"\"\"'F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "SNerro3 c2:=coeff(coeff(SNterm[1],D[3,3](f[1])(x0,y0[1],y0[2])),f[2](x0,y0[1], y0[2])^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNerro3c2G,&*&&%\"bG6 #\"\"#\"\"\"&%\"aG6$F*F+F*#F+F*#!\"\"\"\"'F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "SNerro3c3:=coeff(coeff(coeff(SNterm[1],D[2,3](f [1])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2])),f[1](x0,y0[1],y0[2]));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNerro3c3G,&*&&%\"bG6#\"\"#\"\"\"&% \"aG6$F*F+F*F+#!\"\"\"\"$F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "SNerro3d1:=coeff(coeff(SNterm[1],D[2](f[1])(x0,y0[1],y0[2])),D[1]( f[1])(x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNerro3d 1G#!\"\"\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "SNerro3d2: =coeff(coeff(SNterm[1],D[3](f[1])(x0,y0[1],y0[2])),D[1](f[2])(x0,y0[1] ,y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNerro3d2G#!\"\"\"\"' " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "SNerro3e1:=coeff(coeff( SNterm[1],D[2](f[1])(x0,y0[1],y0[2])^2),f[1](x0,y0[1],y0[2]));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNerro3e1G#!\"\"\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 117 "SNerro3e2:=coeff(coeff(coeff(SNter m[1],D[2](f[1])(x0,y0[1],y0[2])),D[3](f[1])(x0,y0[1],y0[2])),f[2](x0,y 0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNerro3e2G#!\"\"\" \"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 117 "SNerro3e3:=coeff(co eff(coeff(SNterm[1],D[3](f[1])(x0,y0[1],y0[2])),D[2](f[2])(x0,y0[1],y0 [2])),f[1](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNe rro3e3G#!\"\"\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 117 "SNer ro3e4:=coeff(coeff(coeff(SNterm[1],D[3](f[1])(x0,y0[1],y0[2])),D[3](f[ 2])(x0,y0[1],y0[2])),f[2](x0,y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SNerro3e4G#!\"\"\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 28 "# soluciones para el orden 2" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 78 "SNsolve221:=solve(\{SNcond1a,SNcond2a,SNcond2b 1,SNcond2b2\},\{b[1],b[2],a[2,1]\});" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%+SNsolve221G<%/&%\"bG6#\"\"\",$*&,&!\"\"F*&%\"cG6#\"\"#F2F*F/F.#F* F2/&%\"aG6$F2F*F//&F(F1,$*$F/F.F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "SNsolve222:=solve(\{SNcond1a,SNcond2a,SNcond2b1,SNcon d2b2,c[2]=0\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+SNsolve222G6\"" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 24 "# minimizaci\363n del erro r" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 205 "SNerror221:=solve(sub s(SNsolve221,\{SNerro3a,SNerro3b1,SNerro3b2,SNerro3c1,SNerro3c2,SNerro 3c3\})) union subs(solve(subs(SNsolve221,\{SNerro3a,SNerro3b1,SNerro3b 2,SNerro3c1,SNerro3c2,SNerro3c3\})),SNsolve221);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+SNerror221G<&/&%\"cG6#\"\"##F*\"\"$/&%\"bG6#\"\"\"#F 1\"\"%/&%\"aG6$F*F1F+/&F/F)#F,F3" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 30 "# PARA SISTEMAS AUTONOMOS (SA)" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 37 "# desarrollo de la verdadera solucion" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "y[1]:=unapply(y[1](x),x):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "y[2]:=unapply(y[2](x),x):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "f[1]:=unapply(f[1](y[1],y[ 2]),y[1],y[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "f[2]:=un apply(f[2](y[1],y[2]),y[1],y[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "f0[1]:=f[1](y[1](x),y[2](x)):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 29 "f0[2]:=f[2](y[1](x),y[2](x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "f1[1]:=subs(\{diff(y[1](x),x)=f[1] (y[1](x),y[2](x)),diff(y[2](x),x)=f[2](y[1](x),y[2](x))\},diff(f0[1],x )):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "f1[2]:=subs(\{diff( y[1](x),x)=f[1](y[1](x),y[2](x)),diff(y[2](x),x)=f[2](y[1](x),y[2](x)) \},diff(f0[2],x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "f2[1 ]:=subs(\{diff(y[1](x),x)=f[1](y[1](x),y[2](x)),diff(y[2](x),x)=f[2](y [1](x),y[2](x))\},diff(f1[1],x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "f2[2]:=subs(\{diff(y[1](x),x)=f[1](y[1](x),y[2](x)), diff(y[2](x),x)=f[2](y[1](x),y[2](x))\},diff(f1[2],x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f0[1]:=subs(\{y[1](x)=y0[1],y[2](x) =y0[2],x=x0\},f0[1]):SAf0[1]:=expand(f0[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%%SAf0G6#\"\"\"-&%\"fGF&6$&%#y0GF&&F-6#\"\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f0[2]:=subs(\{y[1](x)=y0[1], y[2](x)=y0[2],x=x0\},f0[2]):SAf0[2]:=expand(f0[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f1[1]:=subs(\{y[1](x)=y0[1],y[2](x)=y0[2] ,x=x0\},f1[1]):SAf1[1]:=expand(f1[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%%SAf1G6#\"\"\",&*&--&%\"DGF&6#&%\"fGF&6$&%#y0GF&&F36#\"\"#F'- F/F1F'F'*&--&F-F5F.F1F'-&F0F5F1F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f1[2]:=subs(\{y[1](x)=y0[1],y[2](x)=y0[2],x=x0\},f1[2 ]):SAf1[2]:=expand(f1[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f2[1]:=subs(\{y[1](x)=y0[1],y[2](x)=y0[2],x=x0\},f2[1]):SAf2[1]:=e xpand(f2[1]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%%SAf2G6#\"\"\",0*& --&%\"DG6$F'F'6#&%\"fGF&6$&%#y0GF&&F46#\"\"#F'-F0F2F7F'*(F8F'--&F-6$F' F7F/F2F'-&F1F6F2F'F7*&--&F-F&F/F2F7F8F'F'*(FAF'--&F-F6F/F2F'F>F'F'*&-- &F-6$F7F7F/F2F'F>F7F'*(FEF'--FC6#F?F2F'F8F'F'*(FEF'--FGFPF2F'F>F'F'" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "f2[2]:=subs(\{y[1](x)=y0[1 ],y[2](x)=y0[2],x=x0\},f2[2]):SAf2[2]:=expand(f2[2]):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 23 "# desarrollo del m\351todo" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "k10[1]:=f[1](y[1],y[2]):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "k10[2]:=f[2](y[1],y[2]):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "k20[1]:=f[1](y[1]+a[2,1]*h *k10[1],y[2]+a[2,1]*h*k10[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "k20[2]:=f[2](y[1]+a[2,1]*h*k10[1],y[2]+a[2,1]*h*k10[2]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k100[1]:=subs(h=0,k10[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k100[2]:=subs(h=0,k10[2]) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k200[1]:=subs(h=0,k20[ 1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k200[2]:=subs(h=0,k 20[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "Fi0[1]:=b[1]*k1 00[1]+b[2]*k200[1]:Fi0[1]:=subs(\{x=x0,y[1]=y0[1],y[2]=y0[2]\},Fi0[1]) :SAFi0[1]:=expand(Fi0[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&SAFi 0G6#\"\"\",&*&&%\"bGF&F'-&%\"fGF&6$&%#y0GF&&F16#\"\"#F'F'*&&F+F3F'F,F' F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "Fi0[2]:=b[1]*k100[2] +b[2]*k200[2]:Fi0[2]:=subs(\{x=x0,y[1]=y0[1],y[2]=y0[2]\},Fi0[2]):SAFi 0[2]:=expand(Fi0[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k1 1[1]:=diff(k10[1],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k1 1[2]:=diff(k10[2],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k2 1[1]:=diff(k20[1],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k2 1[2]:=diff(k20[2],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k1 10[1]:=subs(h=0,k11[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k110[2]:=subs(h=0,k11[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k210[1]:=subs(h=0,k21[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k210[2]:=subs(h=0,k21[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "Fi1[1]:=b[1]*k110[1]+b[2]*k210[1]:Fi1[1]:=subs(\{x=x 0,y[1]=y0[1],y[2]=y0[2]\},Fi1[1]):SAFi1[1]:=expand(Fi1[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&SAFi1G6#\"\"\",&**&%\"bG6#\"\"#F'--&%\"D GF&6#&%\"fGF&6$&%#y0GF&&F7F,F'&%\"aG6$F-F'F'-F3F5F'F'**F*F'--&F1F,F2F5 F'F9F'-&F4F,F5F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "Fi1[ 2]:=b[1]*k110[2]+b[2]*k210[2]:Fi1[2]:=subs(\{x=x0,y[1]=y0[1],y[2]=y0[2 ]\},Fi1[2]):SAFi1[2]:=expand(Fi1[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k12[1]:=diff(k11[1],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k12[2]:=diff(k11[2],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k22[1]:=diff(k21[1],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "k22[2]:=diff(k21[2],h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k120[1]:=subs(h=0,k12[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k120[2]:=subs(h=0,k12[2]):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 26 "k220[1]:=subs(h=0,k22[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "k220[2]:=subs(h=0,k22[2]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "Fi2[1]:=b[1]*k120[1]+b[2]*k220[1]: Fi2[1]:=subs(\{x=x0,y[1]=y0[1],y[2]=y0[2]\},Fi2[1]):SAFi2[1]:=expand(F i2[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&SAFi2G6#\"\"\",(**&%\"b G6#\"\"#F'&%\"aG6$F-F'F--&%\"fGF&6$&%#y0GF&&F6F,F---&%\"DG6$F'F'6#F2F4 F'F'*,F*F'F.F-F1F'--&F;6$F'F-F=F4F'-&F3F,F4F'F-**F*F'F.F-FCF---&F;6$F- F-F=F4F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "Fi2[2]:=b[1] *k120[2]+b[2]*k220[2]:Fi2[2]:=subs(\{x=x0,y[1]=y0[1],y[2]=y0[2]\},Fi2[ 2]):SAFi2[1]:=expand(Fi2[1]):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 24 "# consistencia y orden 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "SAcond1a:=coeff(SAFi0[1],f[1](y0[1],y0[2]))=coeff(SAf0[1],f[1] (y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)SAcond1aG/,&&%\" bG6#\"\"\"F*&F(6#\"\"#F*F*" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# condiciones para el orden 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "#SAcond2a" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 146 "SAcond2b1:=coeff(coeff(SAFi1[1],D[1](f[1])(y0[1],y0[2])),f[1](y0[ 1],y0[2]))=coeff(coeff((1/2)*SAf1[1],D[1](f[1])(y0[1],y0[2])),f[1](y0[ 1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAcond2b1G/*&&%\"bG6 #\"\"#\"\"\"&%\"aG6$F*F+F+#F+F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 146 "SAcond2b2:=coeff(coeff(SAFi1[1],D[2](f[1])(y0[1],y0[2])),f[2] (y0[1],y0[2]))=coeff(coeff((1/2)*SAf1[1],D[2](f[1])(y0[1],y0[2])),f[2] (y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAcond2b2G/*&&% \"bG6#\"\"#\"\"\"&%\"aG6$F*F+F+#F+F*" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 34 "# coeficiente del t\351rmino de error" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "SAterm[1]:=expand((1/2!)*SAFi2[1]-( 1/3!)*SAf2[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "#SAerro3a " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAerro3b1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAerro3b2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "SAerro3c1:=coeff(coeff(SAterm[1],D[1,1](f[1])(y0 [1],y0[2])),f[1](y0[1],y0[2])^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %*SAerro3c1G,&*&&%\"bG6#\"\"#\"\"\"&%\"aG6$F*F+F*#F+F*#!\"\"\"\"'F+" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "SAerro3c2:=coeff(coeff(SAt erm[1],D[2,2](f[1])(y0[1],y0[2])),f[2](y0[1],y0[2])^2);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%*SAerro3c2G,&*&&%\"bG6#\"\"#\"\"\"&%\"aG6$F*F+ F*#F+F*#!\"\"\"\"'F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "SA erro3c3:=coeff(coeff(coeff(SAterm[1],D[1,2](f[1])(y0[1],y0[2])),f[2](y 0[1],y0[2])),f[1](y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% *SAerro3c3G,&*&&%\"bG6#\"\"#\"\"\"&%\"aG6$F*F+F*F+#!\"\"\"\"$F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAerro3d1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "#SAerro3d2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "SAerro3e1:=coeff(coeff(SAterm[1],D[1](f[1])(y0[1],y0[ 2])^2),f[1](y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAerr o3e1G#!\"\"\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "SAerro 3e2:=coeff(coeff(coeff(SAterm[1],D[1](f[1])(y0[1],y0[2])),D[2](f[1])(y 0[1],y0[2])),f[2](y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% *SAerro3e2G#!\"\"\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 " SAerro3e3:=coeff(coeff(coeff(SAterm[1],D[2](f[1])(y0[1],y0[2])),D[1](f [2])(y0[1],y0[2])),f[1](y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAerro3e3G#!\"\"\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "SAerro3e4:=coeff(coeff(coeff(SAterm[1],D[2](f[1])(y0[1],y0[2] )),D[2](f[2])(y0[1],y0[2])),f[2](y0[1],y0[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*SAerro3e4G#!\"\"\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 28 "# soluciones para el orden 2" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 79 "SAsolve221:=solve(\{SAcond1a,SAcond2b1,SAcond2 b2,c2=a[2,1]\},\{b[1],b[2],a[2,1]\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+SAsolve221G<%/&%\"bG6#\"\"#,$*$%#c2G!\"\"#\"\"\"F*/&F(6#F0,$*&,& F.F0F-F*F0F-F.F//&%\"aG6$F*F0F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "SAsolve222:=solve(\{SAcond1a,SAcond2b1,SAcond2b2,a[2,1]=0\},\{ b[1],b[2],a[2,1]\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+SAsolve222G 6\"" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 26 "# y minimizaci\363n d el error" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "SAerror221:=sub s(solve(subs(SAsolve221,\{SAerro3c1,SAerro3c2,SAerro3c3\})),SAsolve221 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+SAerror221G<%/&%\"bG6#\"\"\"# F*\"\"%/&%\"aG6$\"\"#F*#F1\"\"$/&F(6#F1#F3F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0" 0 }{VIEWOPTS 1 1 0 3 4 1802 }