{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 "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 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 24 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 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 1 14 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 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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 }{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 }{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 261 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 262 22 "(8) Estabilidad lineal" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 260 15 "Ejercicio 08-13" }} {PARA 4 "" 0 "" {TEXT -1 71 "\nB\372squese el m\351todo de GAUSS de 2 \+ etapas (es decir, el m\351todo impl\355cito" }}{PARA 4 "" 0 "" {TEXT -1 41 "de RUNGE-KUTTA con dos etapas y orden 4) " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 264 5 " " }{XPPEDIT 18 0 "c[ 1];" "6#&%\"cG6#\"\"\"" }{TEXT 265 9 " | " }{XPPEDIT 18 0 "a[11] ;" "6#&%\"aG6#\"#6" }{TEXT 266 8 " " }{XPPEDIT 18 0 "a[12];" "6 #&%\"aG6#\"#7" }}{PARA 4 "" 0 "" {TEXT 267 5 " " }{XPPEDIT 18 0 "c [2]" "6#&%\"cG6#\"\"#" }{TEXT 268 9 " | " }{XPPEDIT 18 0 "a[21]; " "6#&%\"aG6#\"#@" }{TEXT 269 8 " " }{XPPEDIT 18 0 "a[22]" "6#& %\"aG6#\"#A" }}{PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 256 24 "------------------------" }}{PARA 4 "" 0 "" {TEXT 257 19 " \+ | " }{XPPEDIT 18 0 "b[1]" "6#&%\"bG6#\"\"\"" }{TEXT 258 10 " \+ " }{XPPEDIT 18 0 "b[2]" "6#&%\"bG6#\"\"#" }{TEXT 259 1 " " }} {PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 46 "(lo que a ntecede es Ejercicio del cap\355tulo 7)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 77 "Calc\372lese la funci\363n de esta bilidad del m\351todo 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 0 21 37 "# desarrollo de la verdadera solucion" }}}{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 44 "f3 :=subs(diff(y(x),x)=f(x,y(x)),diff(f2,x)):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 43 "f0:=subs(\{y(x)=y0,x=x0\},f0):f0:=expand(f0):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "f1:=subs(\{y(x)=y0,x=x0\},f1 ):f1:=expand(f1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "f2:=su bs(\{y(x)=y0,x=x0\},f2):f2:=expand(f2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "f3:=subs(\{y(x)=y0,x=x0\},f3):f3:=expand(f3):" }}} {EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 23 "# desarrollo del m\351todo" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "k10:=unapply(f(x0+c[1]*h,y 0+a[1,1]*h*kp10(h)+a[1,2]*h*kp20(h)),h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "k20:=unapply(f(x0+c[2]*h,y0+a[2,1]*h*kp10(h)+a[2,2]*h *kp20(h)),h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "k100:=k10( 0):k100:=expand(k100):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "k 200:=k20(0):k200:=expand(k200):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Fi0:=expand(b[1]*k100+b[2]*k200):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 12 "k11:=D(k10):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "k21:=D(k20):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "k11 0:=subs(\{kp10(0)=k100,kp20(0)=k200\},k11(0)):k110:=expand(k110):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "k210:=subs(\{kp10(0)=k100,kp 20(0)=k200\},k21(0)):k210:=expand(k210):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Fi1:=expand(b[1]*k110+b[2]*k210):" }}}{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 98 "k120:=subs(\{D(kp10)(0)=k110,D(kp20)(0)=k210,kp10(0)=k100,kp20(0 )=k200\},k12(0)):k120:=expand(k120):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "k220:=subs(\{D(kp10)(0)=k110,D(kp20)(0)=k210,kp10(0)= k100,kp20(0)=k200\},k22(0)):k220:=expand(k220):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 33 "Fi2:=expand(b[1]*k120+b[2]*k220):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "k13:=D(k12):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 12 "k23:=D(k22):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 140 "k130:=subs(\{(D@@2)(kp10)(0)=k120,(D@@2)(kp20)(0)=k2 20,D(kp10)(0)=k110,D(kp20)(0)=k210,kp10(0)=k100,kp20(0)=k200\},k13(0)) :k130:=expand(k130):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 140 "k2 30:=subs(\{(D@@2)(kp10)(0)=k120,(D@@2)(kp20)(0)=k220,D(kp10)(0)=k110,D (kp20)(0)=k210,kp10(0)=k100,kp20(0)=k200\},k23(0)):k230:=expand(k230): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Fi3:=expand(b[1]*k130+b [2]*k230):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 24 "# consistencia y orden 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "cond1a:=coeff (Fi0,f(x0,y0))=coeff(f0,f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%'cond1aG/,&&%\"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 65 "cond2a:=coeff(Fi1,D[1](f)(x0,y0))=coeff((1/2 )*f1,D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2aG/,& *&&%\"bG6#\"\"\"F+&%\"cGF*F+F+*&&F)6#\"\"#F+&F-F0F+F+#F+F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "cond2b:=coeff(coeff(Fi1,D[2](f)(x0, y0)),f(x0,y0))=coeff(coeff((1/2)*f1,D[2](f)(x0,y0)),f(x0,y0));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2bG/,**&&%\"bG6#\"\"\"F+&%\"aG6 $F+F+F+F+*&F(F+&F-6$F+\"\"#F+F+*&&F)6#F2F+&F-6$F2F+F+F+*&F4F+&F-6$F2F2 F+F+#F+F2" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# condiciones p ara el orden 3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "cond3a:=c oeff(Fi2,D[1,1](f)(x0,y0))=coeff((1/3)*f2,D[1,1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3aG/,&*&&%\"bG6#\"\"\"F+)&%\"cGF*\"\" #F+F+*&&F)6#F/F+)&F.F2F/F+F+#F+\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "cond3b:=coeff(coeff(Fi2,D[1,2](f)(x0,y0)),f(x0,y0))= coeff(coeff((1/3)*f2,D[1,2](f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3bG/,***\"\"#\"\"\"&%\"bG6#F)F)&%\"cGF,F)&%\"aG6 $F)F)F)F)**F(F)F*F)F-F)&F06$F)F(F)F)**F(F)&F+6#F(F)&F.F7F)&F06$F(F)F)F )**F(F)F6F)F8F)&F06$F(F(F)F)#F(\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "cond3c:=coeff(coeff(Fi2,D[2,2](f)(x0,y0)),f(x0,y0)^2 )=coeff(coeff((1/3)*f2,D[2,2](f)(x0,y0)),f(x0,y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3cG/,.*&&%\"bG6#\"\"\"F+)&%\"aG6$F+F+\"\"#F +F+**F0F+F(F+F-F+&F.6$F+F0F+F+*&F(F+)F2F0F+F+*&&F)6#F0F+)&F.6$F0F+F0F+ F+**F0F+F7F+F:F+&F.6$F0F0F+F+*&F7F+)F=F0F+F+#F+\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "cond3d:=coeff(coeff(Fi2,D[2](f)(x0,y0)), D[1](f)(x0,y0))=coeff(coeff((1/3)*f2,D[2](f)(x0,y0)),D[1](f)(x0,y0)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3dG/,***\"\"#\"\"\"&%\"bG6# F)F)&%\"cGF,F)&%\"aG6$F)F)F)F)**F(F)F*F)&F06$F)F(F)&F.6#F(F)F)**F(F)&F +F6F)&F06$F(F)F)F-F)F)**F(F)F8F)F5F)&F06$F(F(F)F)#F)\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "cond3e:=coeff(coeff(Fi2,D[2](f)(x0 ,y0)^2),f(x0,y0))=coeff(coeff((1/3)*f2,D[2](f)(x0,y0)^2),f(x0,y0));" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3eG/,2*(\"\"#\"\"\"&%\"bG6#F)F ))&%\"aG6$F)F)F(F)F)**F(F)F*F)F.F)&F/6$F)F(F)F)**F(F)F*F)F2F)&F/6$F(F) F)F)**F(F)F*F)F2F)&F/6$F(F(F)F)**F(F)&F+6#F(F)F5F)F.F)F)**F(F)F;F)F2F) F5F)F)**F(F)F;F)F5F)F8F)F)*(F(F)F;F))F8F(F)F)#F)\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# condiciones para el orden 4" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "cond4a:=coeff(Fi3,D[1,1,1](f )(x0,y0))=coeff((1/4)*f3,D[1,1,1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4aG/,&*&&%\"bG6#\"\"#\"\"\")&%\"cGF*\"\"$F,F,*&& F)6#F,F,)&F/F3F0F,F,#F,\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "cond4b:=coeff(coeff(Fi3,D[1,1,2](f)(x0,y0)),f(x0,y0))=coeff(coe ff((1/4)*f3,D[1,1,2](f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4bG/,***\"\"$\"\"\"&%\"bG6#\"\"#F))&%\"cGF,F-F)& %\"aG6$F-F-F)F)**F(F)&F+6#F)F))&F0F6F-F)&F26$F)F)F)F)**F(F)F5F)F7F)&F2 6$F)F-F)F)**F(F)F*F)F.F)&F26$F-F)F)F)#F(\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "cond4c:=coeff(coeff(Fi3,D[1,2,2](f)(x0,y0)),f(x 0,y0)^2)=coeff(coeff((1/4)*f3,D[1,2,2](f)(x0,y0)),f(x0,y0)^2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4cG/,.**\"\"$\"\"\"&%\"bG6#\"\" #F)&%\"cGF,F))&%\"aG6$F-F-F-F)F)*,\"\"'F)&F+6#F)F)&F/F7F)&F26$F)F)F)&F 26$F)F-F)F)**F(F)F6F)F8F))F9F-F)F)**F(F)F6F)F8F))F;F-F)F)**F(F)F*F)F.F ))&F26$F-F)F-F)F)*,F5F)F*F)F.F)FCF)F1F)F)#F(\"\"%" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 113 "cond4d:=coeff(coeff(Fi3,D[1,2](f)(x0,y0)),D [1](f)(x0,y0))=coeff(coeff((1/4)*f3,D[1,2](f)(x0,y0)),D[1](f)(x0,y0)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4dG/,***\"\"'\"\"\"&%\"bG6# F)F))&%\"cGF,\"\"#F)&%\"aG6$F)F)F)F)*,F(F)F*F)F.F)&F26$F)F0F)&F/6#F0F) F)**F(F)&F+F8F))F7F0F)&F26$F0F0F)F)*,F(F)F:F)F7F)&F26$F0F)F)F.F)F)#\" \"$\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 145 "cond4e:=coeff( coeff(coeff(Fi3,D[1,2](f)(x0,y0)),D[2](f)(x0,y0)),f(x0,y0))=coeff(coef f(coeff((1/4)*f3,D[1,2](f)(x0,y0)),D[2](f)(x0,y0)),f(x0,y0));" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%'cond4eG/,:*,\"\"'\"\"\"&%\"bG6#\"\" #F)&%\"cG6#F)F)&%\"aG6$F)F-F)&F26$F-F)F)F)*,F(F)&F+F0F)F1F)&F/F,F)&F26 $F-F-F)F)*,F(F)F7F)F1F)F8F)F4F)F)*,F(F)F7F)F.F)F1F)F9F)F)*,F(F)F7F)F.F )F1F)F4F)F)*,\"#7F)F7F)F.F)&F26$F)F)F)F1F)F)*,F(F)F*F)F4F)F.F)F@F)F)*, F?F)F*F)F8F)F4F)F9F)F)*,F(F)F*F)F8F)F4F)F@F)F)*,F(F)F*F)F1F)F8F)F4F)F) **F?F)F7F)F.F))F@F-F)F)**F?F)F*F)F8F))F9F-F)F)#\"\"&\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "cond4f:=coeff(coeff(Fi3,D[2,2,2](f )(x0,y0)),f(x0,y0)^3)=coeff(coeff((1/4)*f3,D[2,2,2](f)(x0,y0)),f(x0,y0 )^3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4fG/,2**\"\"$\"\"\"&% \"bG6#\"\"#F)&%\"aG6$F-F)F))&F/6$F-F-F-F)F)*&&F+6#F)F))&F/6$F)F-F(F)F) *&F5F))&F/6$F)F)F(F)F)*&F*F))F.F(F)F)*&F*F))F2F(F)F)**F(F)F*F))F.F-F)F 2F)F)**F(F)F5F))F " 0 "" {MPLTEXT 1 0 145 "cond4g:=coeff(coeff(coeff(F i3,D[2,2](f)(x0,y0)),D[1](f)(x0,y0)),f(x0,y0))=coeff(coeff(coeff((1/4) *f3,D[2,2](f)(x0,y0)),D[1](f)(x0,y0)),f(x0,y0));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'cond4gG/,2*,\"\"'\"\"\"&%\"bG6#\"\"#F)&%\"cGF,F)&%\" aG6$F-F)F)&F16$F-F-F)F)**F(F)F*F)F.F))F3F-F)F)**F(F)F*F))F0F-F)&F/6#F) F)F)**F(F)&F+F:F)F9F))&F16$F)F)F-F)F)*,F(F)FF)&F16$F)F-F)F)*, F(F)FF)F)**F(F)F " 0 "" {MPLTEXT 1 0 149 "cond4h:=coef f(coeff(coeff(Fi3,D[2,2](f)(x0,y0)),D[2](f)(x0,y0)),f(x0,y0)^2)=coeff( coeff(coeff((1/4)*f3,D[2,2](f)(x0,y0)),D[2](f)(x0,y0)),f(x0,y0)^2);" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'cond4hG/,J**\"#=\"\"\"&%\"bG6#F)F) )&%\"aG6$F)F)\"\"#F)&F/6$F)F1F)F)**\"\"*F)F*F)F.F))F2F1F)F)**\"\"'F)F* F)F6F)&F/6$F1F)F)F)**F8F)F*F)F6F)&F/6$F1F1F)F)*,F8F)F*F)F2F)F9F)F.F)F) *,F8F)F*F)F2F)F " 0 "" {MPLTEXT 1 0 113 "cond4i:=coeff(coeff(Fi3,D[1,1](f)( x0,y0)),D[2](f)(x0,y0))=coeff(coeff((1/4)*f3,D[1,1](f)(x0,y0)),D[2](f) (x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4iG/,***\"\"$\"\" \"&%\"bG6#F)F)&%\"aG6$F)\"\"#F))&%\"cG6#F0F0F)F)**F(F)F*F))&F3F,F0F)&F .6$F)F)F)F)**F(F)&F+F4F)&F.6$F0F)F)F6F)F)**F(F)F;F)F1F)&F.6$F0F0F)F)#F )\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "cond4j:=coeff(co eff(Fi3,D[1](f)(x0,y0)),D[2](f)(x0,y0)^2)=coeff(coeff((1/4)*f3,D[1](f) (x0,y0)),D[2](f)(x0,y0)^2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'cond 4jG/,2*,\"\"'\"\"\"&%\"bG6#\"\"#F)&%\"aG6$F)F-F)&%\"cGF,F)&F/6$F-F)F)F )*,F(F)&F+6#F)F)&F2F7F)F.F)F3F)F)*,F(F)F*F)F3F)F8F)&F/6$F)F)F)F)*,F(F) F*F)F3F)F8F)&F/6$F-F-F)F)**F(F)F6F)F8F))F:F-F)F)*,F(F)F6F)F.F)F1F)F:F) F)*,F(F)F6F)F.F)F1F)F=F)F)**F(F)F*F)F1F))F=F-F)F)#F)\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "cond4k:=coeff(coeff(Fi3,D[2](f)(x0 ,y0)^3),f(x0,y0))=coeff(coeff((1/4)*f3,D[2](f)(x0,y0)^3),f(x0,y0));" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'cond4kG/,>*(\"\"'\"\"\"&%\"bG6#F)F ))&%\"aG6$F)F)\"\"$F)F)*(F(F)&F+6#\"\"#F))&F/6$F5F5F1F)F)*,F(F)F3F)&F/ 6$F)F5F)&F/6$F5F)F)F.F)F)*,\"#7F)F3F)F:F)F " 0 "" {MPLTEXT 1 0 160 "metodo:=a llvalues(solve(\{cond1a,cond2a,cond2b,cond3a,cond3b,cond3c,cond3d,cond 3e,cond4a,cond4b,cond4c,cond4d,cond4f,c[1]=a[1,1]+a[1,2],c[2]=a[2,1]+a [2,2]\}))[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'metodoG<*/&%\"bG6# \"\"\"#F*\"\"#/&F(6#F,F+/&%\"aG6$F*F*#F*\"\"%/&F26$F,F,F4/&%\"cGF),&F+ F**&\"\"'!\"\"\"\"$F+F?/&F;F/,&F+F**&F>F?F@F+F*/&F26$F*F,,&F4F**&F>F?F @F+F?/&F26$F,F*,&F4F**&F>F?F@F+F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 208 "c[1]:=subs(metodo,c[1]);c[2]:=subs(metodo,c[2]);a[1, 1]:=subs(metodo,a[1,1]);a[1,2]:=subs(metodo,a[1,2]);a[2,1]:=subs(metod o,a[2,1]);a[2,2]:=subs(metodo,a[2,2]);b[1]:=subs(metodo,b[1]);b[2]:=su bs(metodo,b[2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"cG6#\"\"\",&# F'\"\"#F'*&\"\"'!\"\"\"\"$F)F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&% \"cG6#\"\"#,&#\"\"\"F'F**&\"\"'!\"\"\"\"$F)F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"aG6$\"\"\"F'#F'\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"aG6$\"\"\"\"\"#,&#F'\"\"%F'*&\"\"'!\"\"\"\"$#F'F(F." }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"aG6$\"\"#\"\"\",&#F(\"\"%F(*&\"\" '!\"\"\"\"$#F(F'F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"aG6$\"\"#F' #\"\"\"\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"bG6#\"\"\"#F'\"\" #" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"bG6#\"\"##\"\"\"F'" }}} {EXCHG {PARA 4 "" 0 "" {TEXT -1 53 "Significa esto que el m\351todo de GAUSS de 2 etapas es " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 274 5 " " }{XPPEDIT 18 0 "(3-sqrt(3))/6;" "6#*&,&\"\"$ \"\"\"-%%sqrtG6#F%!\"\"F&\"\"'F*" }{TEXT 275 15 " | " } {XPPEDIT 18 0 "1/4;" "6#*&\"\"\"F$\"\"%!\"\"" }{TEXT 276 18 " \+ " }{XPPEDIT 18 0 "(3-2*sqrt(3))/12;" "6#*&,&\"\"$\"\"\"*&\"\" #F&-%%sqrtG6#F%F&!\"\"F&\"#7F," }}{PARA 4 "" 0 "" {TEXT 277 5 " " }{XPPEDIT 18 0 "(3+sqrt(3))/6;" "6#*&,&\"\"$\"\"\"-%%sqrtG6#F%F&F&\"\" '!\"\"" }{TEXT 278 9 " | " }{XPPEDIT 18 0 "(3+2*sqrt(3))/12;" "6 #*&,&\"\"$\"\"\"*&\"\"#F&-%%sqrtG6#F%F&F&F&\"#7!\"\"" }{TEXT 279 18 " \+ " }{XPPEDIT 18 0 "1/4;" "6#*&\"\"\"F$\"\"%!\"\"" }} {PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 270 44 "------------ --------------------------------" }}{PARA 4 "" 0 "" {TEXT 271 33 " \+ | " }{XPPEDIT 18 0 "1/2;" "6#*&\"\"\"F$\"\" #!\"\"" }{TEXT 272 24 " " }{XPPEDIT 18 0 "1/2; " "6#*&\"\"\"F$\"\"#!\"\"" }{TEXT 273 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 24 "# funcion de estab ilidad" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=(x,y)->lambda* y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"xG%\"yG6\"6$%)opera torG%&arrowGF)*&%'lambdaG\"\"\"9%F/F)F)F)" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 64 "ka1:=unapply(f(x0+c[1]*h,y0+a[1,1]*h*kp1(h)+a[1,2]* h*kp2(h)),h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ka1Gf*6#%\"hG6\"6$ %)operatorG%&arrowGF(*&%'lambdaG\"\"\",(%#y0GF.*&#F.\"\"%F.*&9$F.-%$kp 1G6#F5F.F.F.*(,&F2F.*&\"\"'!\"\"\"\"$#F.\"\"#F=F.F5F.-%$kp2GF8F.F.F.F( F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "ka2:=unapply(f(x0+c [2]*h,y0+a[2,1]*h*kp1(h)+a[2,2]*h*kp2(h)),h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ka2Gf*6#%\"hG6\"6$%)operatorG%&arrowGF(*&%'lambdaG\" \"\",(%#y0GF.*(,&#F.\"\"%F.*&\"\"'!\"\"\"\"$#F.\"\"#F.F.9$F.-%$kp1G6#F ;F.F.*&F3F.*&F;F.-%$kp2GF>F.F.F.F.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "test:=solve(\{k1=subs(\{kp1(h)=k1,kp2(h)=k2\},ka1(h)) ,k2=subs(\{kp1(h)=k1,kp2(h)=k2\},ka2(h))\},\{k1,k2\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%testG<$/%#k2G,$*.\"\"#\"\"\"\"\"$#F+F*%'lambdaG F+%#y0GF+,&*&F.F+%\"hGF+F+*&F*F+F,F-F+F+,(*(\"\"'F+F.F+F2F+!\"\"\"#7F+ *&)F.F*F+)F2F*F+F+F7F+/%#k1G,$*.F*F+F,F-F.F+F/F+,&*&F*F+F,F-F7F1F+F+F4 F7F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "k1:=subs(test,k1);k 2:=subs(test,k2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k1G,$*.\"\"#\" \"\"\"\"$#F(F'%'lambdaGF(%#y0GF(,&*&F'F(F)F*!\"\"*&F+F(%\"hGF(F(F(,(*( \"\"'F(F+F(F1F(F/\"#7F(*&)F+F'F()F1F'F(F(F/F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k2G,$*.\"\"#\"\"\"\"\"$#F(F'%'lambdaGF(%#y0GF(,&*&F+ F(%\"hGF(F(*&F'F(F)F*F(F(,(*(\"\"'F(F+F(F/F(!\"\"\"#7F(*&)F+F'F()F/F'F (F(F4F(" }}}{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\" \"\"*,\"#7F'%\"hGF'%'lambdaGF'F&F',(*(\"\"'F'F+F'F*F'!\"\"F)F'*&)F+\" \"#F')F*F2F'F'F/F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "y1:=c ollect(subs(lambda=z/h,y1),y0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%# y1G*&,&\"\"\"F'*(\"#7F'%\"zGF',(*&\"\"'F'F*F'!\"\"F)F'*$)F*\"\"#F'F'F. F'F'%#y0GF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "r:=unapply(c ollect(simplify(y1/y0),z),z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"r Gf*6#%\"zG6\"6$%)operatorG%&arrowGF(*&,(*&\"\"'\"\"\"9$F0F0\"#7F0*$)F1 \"\"#F0F0F0,(*&F/F0F1F0!\"\"F2F0F3F0F8F(F(F(" }}}{EXCHG {PARA 4 "" 0 " " {TEXT 263 65 "que es la funci\363n de estabilidad del m\351todo de G AUSS de 2 etapas." }}{PARA 4 "" 0 "" {TEXT 280 50 "Como las ra\355ces \+ del numerador de r son -3 +- i " }{XPPEDIT 18 0 "sqrt(3);" "6#-%%sq rtG6#\"\"$" }{TEXT -1 13 " y las del " }}{PARA 4 "" 0 "" {TEXT -1 18 "denominador son " }{TEXT 281 7 "3 +- i " }{XPPEDIT 18 0 "sqrt(3) ;" "6#-%%sqrtG6#\"\"$" }{TEXT -1 14 " , tenemos que" }}{PARA 4 "" 0 " " {TEXT -1 4 " " }{TEXT 282 11 " " }{TEXT -1 11 " \+ " }{XPPEDIT 18 0 "(z+3-i*sqrt(3))*(z+3+i*sqrt(3))/((z-3-i*sqrt(3))* (z-3+i*sqrt(3)));" "6#*(,(%\"zG\"\"\"\"\"$F&*&%\"iGF&-%%sqrtG6#F'F&!\" \"F&,(F%F&F'F&*&F)F&-F+6#F'F&F&F&*&,(F%F&F'F-*&F)F&-F+6#F'F&F-F&,(F%F& F'F-*&F)F&-F+6#F'F&F&F&F-" }{TEXT -1 6 " = " }{XPPEDIT 18 0 "((z+3) ^2+3)/((z-3)^2+3);" "6#*&,&*$,&%\"zG\"\"\"\"\"$F(\"\"#F(F)F(F(,&*$,&F' F(F)!\"\"F*F(F)F(F." }{TEXT -1 7 " " }}{PARA 4 "" 0 "" {TEXT -1 101 "Para z real, (z + 3)^2 es el cuadrado de la distancia de z a \+ -3 y lo an\341logo con (z - 3)^2 y 3" }}{PARA 4 "" 0 "" {TEXT -1 91 "Los n\372meros reales negativos est\341n en el dominio D y los p ositivos en su complementario. " }}{PARA 4 "" 0 "" {TEXT -1 84 "Pero n o hay en el caso complejo la misma interpretaci\363n sobre la distanci a mientras " }}{PARA 4 "" 0 "" {TEXT -1 93 "no intervenga el m\363dulo , as\355 que todav\355a no podemos concluir si el m\351todo es o no A- estable. " }}{PARA 4 "" 0 "" {TEXT -1 96 "Vamos a construir la fronter a de D de ecuaci\363n | r(z) |^2 = 1 en el plano complejo, o lo qu e" }}{PARA 4 "" 0 "" {TEXT -1 11 "es lo mismo" }}{PARA 4 "" 0 "" {TEXT -1 43 " |(z + 3)^2 + 3|^2 = |(z - 3)^2 + 3|^2" }}{PARA 4 " " 0 "" {TEXT 283 42 "poniendo z=x+i y , lo anterior se escribe" }} {PARA 4 "" 0 "" {TEXT 284 92 " ((x + 3)^2 - y^2 + 3)^2 + 4 y^2 (x + 3)^2 = ((x - 3)^2 - y^2 + 3)^2 + 4 y^2 (x - 3)^2 " }}{PARA 4 "" 0 " " {TEXT 285 16 "o simplificando " }}{PARA 4 "" 0 "" {TEXT 286 38 " \+ 24 x^3 + 288 x + 24 x y^2 = 0 " }}{PARA 4 "" 0 "" {TEXT 287 35 " \+ x (24 x^2 + 288 + 24 y^2) = 0" }}{PARA 4 "" 0 "" {TEXT 288 94 "y l a curva frontera del dominio se compone s\363lo de los puntos con x = 0, o sea, los z = i y, " }}{PARA 4 "" 0 "" {TEXT 289 42 "ya que la ex presi\363n 24 x^2 + 288 + 24 y^2" }{TEXT 290 189 " no puede anularse .\nQueda por determinar cu\341l de los dos semiplanos\n Re(z) < 0 o Re(z) > 0\nseparados por la curva que hemos calculado, es el domi nio de estabilidad. Pues bien, como " }}{PARA 4 "" 0 "" {TEXT 291 19 " r (-3) = 3/39 , " }}{PARA 4 "" 0 "" {TEXT 292 127 "-3 est\341 en D , y D coincide exactamente con el semiplano Re(z) < 0 , por lo que el\nM\351todo de Gauss de 2 etapas es A-estable" }{TEXT -1 0 "" }}}} {MARK "0 3 0" 15 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }