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{SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 262 14 "Ejercicios de " }}{PARA 
4 "" 0 "" {TEXT 268 22 "(8) Estabilidad lineal" }}{PARA 4 "" 0 "" 
{TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 267 15 "Ejercicio 08-15" }}
{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 73 "Est\372di
ese si el m\351todo diagonalmente impl\355cito de RUNGE-KUTTA del tabl
ero" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 256 5 "  \+
   " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT 269 15 "    |        \+
  " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT 270 18 "              \+
   0" }}{PARA 4 "" 0 "" {TEXT 257 19 "      1    |       " }{XPPEDIT 
18 0 "1-alpha;" "6#,&\"\"\"F$%&alphaG!\"\"" }{TEXT 266 13 "           \+
  " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }}{PARA 4 "" 0 "" {TEXT -1 
12 "   ---------" }{TEXT 258 32 "--------------------------------" }}
{PARA 4 "" 0 "" {TEXT 259 16 "           |    " }{XPPEDIT 18 0 "1/(2*(
1-alpha));" "6#*&\"\"\"F$*&\"\"#F$,&F$F$%&alphaG!\"\"F$F)" }{TEXT 260 
5 "     " }{XPPEDIT 18 0 "(1-2*alpha)/(2*(1-alpha));" "6#*&,&\"\"\"F%*
&\"\"#F%%&alphaGF%!\"\"F%*&F'F%,&F%F%F(F)F%F)" }{TEXT 275 3 "   " }
{TEXT 271 4 "    " }}{PARA 4 "" 0 "" {TEXT -1 37 "es o no A-estable. (
Est\341 hecho para  " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT -1 
4 " = 1" }{TEXT -1 3 ")  " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 
"restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface(labe
ling=false):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 261 23 "funci\363n de es
tabilidad " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "f:=(x,y)->lam
bda*y;alpha:=1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"xG%\"y
G6\"6$%)operatorG%&arrowGF)*&%'lambdaG\"\"\"9%F/F)F)F)" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%&alphaG\"\"\"" }}}{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%&arro
wGF(*&%'lambdaG\"\"\",&%#y0GF.*&9$F.-%$kp1G6#F2F.F.F.F(F(F(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "ka2:=unapply(f(x0+2*h,y0+(1-
alpha)*h*kp1(h)+alpha*h*kp2(h)),h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%$ka2Gf*6#%\"hG6\"6$%)operatorG%&arrowGF(*&%'lambdaG\"\"\",&%#y0GF.*
&9$F.-%$kp2G6#F2F.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<$/%#k2G,$*(%'lambdaG\"\"\"%#y0GF+,&!\"\"F+*&F*
F+%\"hGF+F+F.F./%#k1GF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "
k1:=subs(test,k1);k2:=subs(test,k2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%#k1G,$*(%'lambdaG\"\"\"%#y0GF(,&!\"\"F(*&F'F(%\"hGF(F(F+F+" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k2G,$*(%'lambdaG\"\"\"%#y0GF(,&!\"
\"F(*&F'F(%\"hGF(F(F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "
y1:=expand(y0+h*((1/2)*k1+(1/2)*k2));" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%#y1G,&%#y0G\"\"\"**%\"hGF'%'lambdaGF'F&F',&!\"\"F'*&F*F'F)F'F'F,F
," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "y1:=collect(subs(lambd
a=z/h,y1),y0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G*&,&\"\"\"F'*&
%\"zGF',&!\"\"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$%)operatorG%&arrowGF(,$*
&\"\"\"F.,&!\"\"F.9$F.F0F0F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 263 
39 "es la funci\363n de estabilidad del m\351todo" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT 272 25 "A-estabilidad del m\351todo " }}}{EXCHG {PARA 0 "
" 0 "" {TEXT 264 54 "El dominio de estabilidad est\341 compuesto por l
os  z = " }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT 265 47 "  h  ta
les que el m\363dulo de  z-1  sea superior " }}{PARA 0 "" 0 "" {TEXT 
273 102 "a  1 , o sea, por los  z  tales que su distancia al punto  1 \+
 sea superior a 1 . Eso es el exterior de" }}{PARA 0 "" 0 "" {TEXT 
276 99 "la circunferencia de centro  1  y de radio  1 , lo que signifi
ca que contiene al semiplano de parte" }}{PARA 0 "" 0 "" {TEXT 274 51 
"real negativa; por lo tanto, el m\351todo es A-estable" }}}}{MARK "0 \+
3 0" 15 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }