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{SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 263 14 "Ejercicios de " }}{PARA 
4 "" 0 "" {TEXT 264 22 "(8) Estabilidad lineal" }}{PARA 4 "" 0 "" 
{TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 265 51 "Ejercicio 08-12   (del E
XAMEN ORDINARIO de 04FEB08)" }{TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 
-1 52 "\nPara el m\351todo impl\355cito de RUNGE-KUTTA de tablero " }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 260 6 "      " }
{XPPEDIT 18 0 "1/2;" "6#*&\"\"\"F$\"\"#!\"\"" }{TEXT 266 10 "    |    \+
 " }{XPPEDIT 18 0 "1/2" "6#*&\"\"\"F$\"\"#!\"\"" }{TEXT 267 9 "       \+
 0" }}{PARA 4 "" 0 "" {TEXT 261 17 "      1    |     " }{XPPEDIT 18 0 
"1/2" "6#*&\"\"\"F$\"\"#!\"\"" }{TEXT 268 8 "        " }{XPPEDIT 18 0 
"1/2" "6#*&\"\"\"F$\"\"#!\"\"" }}{PARA 4 "" 0 "" {TEXT -1 12 "   -----
----" }{TEXT 256 17 "-----------------" }}{PARA 4 "" 0 "" {TEXT 257 
17 "            |    " }{XPPEDIT 18 0 "1/2;" "6#*&\"\"\"F$\"\"#!\"\"" 
}{TEXT 258 9 "         " }{XPPEDIT 18 0 "1/2;" "6#*&\"\"\"F$\"\"#!\"\"
" }{TEXT 262 4 "    " }}{PARA 4 "" 0 "" {TEXT -1 70 "dib\372jese el co
ntorno de la regi\363n de estabilidad y d\355gase si el m\351todo" }}
{PARA 4 "" 0 "" {TEXT -1 17 "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 0 21 24 "# funcion de estabilidad" }}}{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 84 "c[1]:=1/2:c[2]
:=1:a[1,1]:=1/2:a[1,2]:=0:a[2,1]:=1/2:a[2,2]:=1/2:b[1]:=1/2:b[2]:=1/2:
" }}}{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$F.-%$kp1G6#F5F.F.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#>%$ka
2Gf*6#%\"hG6\"6$%)operatorG%&arrowGF(*&%'lambdaG\"\"\",(%#y0GF.*&#F.\"
\"#F.*&9$F.-%$kp1G6#F5F.F.F.*&F2F.*&F5F.-%$kp2GF8F.F.F.F.F(F(F(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "test:=solve(\{k1=subs(\{kp1(
h)=k1,kp2(h)=k2\},ka1(h)),k2=subs(\{kp1(h)=k1,kp2(h)=k2\},ka2(h))\},\{
k1,k2\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%testG<$/%#k1G,$**\"\"#
\"\"\"%'lambdaGF+%#y0GF+,&F*!\"\"*&F,F+%\"hGF+F+F/F//%#k2G,$**\"\"%F+F
,F+F-F+,(F6F+*(F6F+F,F+F1F+F/*&)F,F*F+)F1F*F+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,$**\"\"#\"\"\"%'lambdaGF(%#y0GF
(,&F'!\"\"*&F)F(%\"hGF(F(F,F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k2
G,$**\"\"%\"\"\"%'lambdaGF(%#y0GF(,(F'F(*(F'F(F)F(%\"hGF(!\"\"*&)F)\"
\"#F()F-F1F(F(F.F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "y1:=e
xpand(y0+h*(b[1]*k1+b[2]*k2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y
1G,(%#y0G\"\"\"**%\"hGF'%'lambdaGF'F&F',&\"\"#!\"\"*&F*F'F)F'F'F-F-*,F
,F'F)F'F*F'F&F',(\"\"%F'*(F1F'F*F'F)F'F-*&)F*F,F')F)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'*&%\"zGF
',&\"\"#!\"\"F)F'F,F,*(F+F'F)F',(\"\"%F'*&F/F'F)F'F,*$)F)F+F'F'F,F'F'%
#y0GF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "r:=unapply(collec
t(simplify(y1/y0),z),z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rGf*6#
%\"zG6\"6$%)operatorG%&arrowGF(,$*&\"\"%\"\"\",(F.F/*&F.F/9$F/!\"\"*$)
F2\"\"#F/F/F3F/F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
}}{EXCHG {PARA 4 "" 0 "" {TEXT 259 6 "O sea " }}{PARA 4 "" 0 "" {TEXT 
270 10 "   r(z) = " }{XPPEDIT 18 0 "4/((z-2)^2);" "6#*&\"\"%\"\"\"*$,&
%\"zGF%\"\"#!\"\"F)F*" }{TEXT 271 8 "        " }}{PARA 4 "" 0 "" 
{TEXT -1 43 "El contorno de la regi\363n de estabilidad es " }}{PARA 
4 "" 0 "" {TEXT -1 8 "   4 =  " }{XPPEDIT 18 0 "abs(z-2)^2;" "6#*$-%$a
bsG6#,&%\"zG\"\"\"\"\"#!\"\"F*" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }
{TEXT 269 8 "o sea   " }}{PARA 4 "" 0 "" {TEXT -1 8 "   2 =  " }
{XPPEDIT 18 0 "abs(z-2);" "6#-%$absG6#,&%\"zG\"\"\"\"\"#!\"\"" }{TEXT 
273 2 "  " }}{PARA 4 "" 0 "" {TEXT 274 64 "circunferencia de centro  2
  y radio  2 . Como adem\341s el punto  " }}{PARA 4 "" 0 "" {TEXT 275 
9 "   z = -1" }{TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 272 50 "est\341 e
n el dominio de estabilidad ya que  r(-1) = " }{XPPEDIT 18 0 "4/9;" "6
#*&\"\"%\"\"\"\"\"*!\"\"" }{TEXT 276 14 " , resulta que" }}{PARA 4 "" 
0 "" {TEXT 277 66 "el dominio de estabilidad es el exterior de esta ci
rcunferencia y " }}{PARA 4 "" 0 "" {TEXT 278 27 "el m\351todo es  A-es
table.   " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 \+
0 0" 6 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }