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{SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 261 14 "Ejercicios de " }}{PARA 
4 "" 0 "" {TEXT 262 55 "(7) M\351todos de RUNGE-KUTTA impl\355citos y \+
semi-impl\355citos" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" 
{TEXT 260 15 "Ejercicio 07-03" }}{PARA 4 "" 0 "" {TEXT -1 71 "\nB\372s
quese 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 40 "(desde aqu\355 es Ejercicio del cap\355
tulo 8)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 
77 "Calc\372lese la funci\363n de estabilidad 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(labe
ling=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:=s
ubs(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:=sub
s(\{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:=subs(\{y(x)=y0,x=x0\},f2
):f2:=expand(f2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "f3:=su
bs(\{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,y0+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(k1
00):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "k200:=k20(0):k200:=
expand(k200):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Fi0:=expan
d(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 "k110:=subs(\{kp10(0)=k
100,kp20(0)=k200\},k11(0)):k110:=expand(k110):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 66 "k210:=subs(\{kp10(0)=k100,kp20(0)=k200\},k21(0
)):k210:=expand(k210):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "F
i1:=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\},k1
2(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)=k220,D(kp10)(
0)=k110,D(kp20)(0)=k210,kp10(0)=k100,kp20(0)=k200\},k13(0)):k130:=expa
nd(k130):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 140 "k230:=subs(\{
(D@@2)(kp10)(0)=k120,(D@@2)(kp20)(0)=k220,D(kp10)(0)=k110,D(kp20)(0)=k
210,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]*k
230):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 24 "# consistencia y or
den 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#>%'co
nd1aG/,&&%\"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)F))&%\"cGF,\"\"#F)&
%\"aG6$F)F)F)F)**F(F)F*F)F-F)&F26$F)F0F)F)**F(F)&F+6#F0F))&F/F9F0F)&F2
6$F0F)F)F)**F(F)F8F)F:F)&F26$F0F0F)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/,.**\"\"$\"\"\"&%\"bG6#F)F)
&%\"cGF,F))&%\"aG6$F)F)\"\"#F)F)**F(F)F*F)F-F))&F16$F)F3F3F)F)*,\"\"'F
)F*F)F-F)F0F)F6F)F)**F(F)&F+6#F3F)&F.F<F))&F16$F3F)F3F)F)**F(F)F;F)F=F
))&F16$F3F3F3F)F)*,F9F)F;F)F=F)F?F)FCF)F)#F(\"\"%" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 113 "cond4d:=coeff(coeff(Fi3,D[1,2](f)(x0,y0)),D
[1](f)(x0,y0))=coeff(coeff((1/4)*f3,D[1,2](f)(x0,y0)),D[1](f)(x0,y0));
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4dG/,***\"\"'\"\"\"&%\"bG6#
\"\"#F))&%\"cGF,F-F)&%\"aG6$F-F-F)F)*,F(F)F*F)F/F)&F26$F-F)F)&F06#F)F)
F)*,F(F)&F+F8F)F7F)&F26$F)F-F)F/F)F)**F(F)F:F))F7F-F)&F26$F)F)F)F)#\"
\"$\"\"%" }}}{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)&%\"aG6$F-F)F)&%\"cG6#F)F)&F/6$F)F)F)F)*,F(F)F*F)F1F)&F/6$F)F-F)F.F
)F)*,F(F)F*F)F7F)&F2F,F)F.F)F)*,F(F)F*F)F:F)F.F)F4F)F)*,\"#7F)F*F)F:F)
F.F)&F/6$F-F-F)F)**F=F)&F+F3F)F1F))F4F-F)F)*,F(F)FAF)F1F)F7F)F.F)F)*,F
=F)FAF)F1F)F4F)F7F)F)*,F(F)FAF)F1F)F7F)F>F)F)*,F(F)FAF)F7F)F:F)F.F)F)*
,F(F)FAF)F7F)F:F)F>F)F)**F=F)F*F)F:F))F>F-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**\"\"$\"\"\"&%
\"bG6#F)F))&%\"aG6$F)F)\"\"#F)&F/6$F)F1F)F)**F(F)F*F)F.F))F2F1F)F)*&F*
F))F.F(F)F)*&F*F))F2F(F)F)*&&F+6#F1F))&F/6$F1F)F(F)F)*&F;F))&F/6$F1F1F
(F)F)**F(F)F;F))F>F1F)FBF)F)**F(F)F;F)F>F))FBF1F)F)#F)\"\"%" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 145 "cond4g:=coeff(coeff(coeff(F
i3,D[2,2](f)(x0,y0)),D[1](f)(x0,y0)),f(x0,y0))=coeff(coeff(coeff((1/4)
*f3,D[2,2](f)(x0,y0)),D[1](f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%'cond4gG/,2*,\"\"'\"\"\"&%\"bG6#\"\"#F)&%\"cGF,F)&%\"
aG6$F-F)F)&F16$F-F-F)F)**F(F)F*F)F.F))F3F-F)F)**F(F)&F+6#F)F))&F16$F)F
-F-F)F.F)F)**F(F)F8F)&F/F9F))&F16$F)F)F-F)F)*,F(F)F8F)F>F)F@F)F;F)F)*,
F(F)F8F)F;F)F.F)F@F)F)*,F(F)F*F)F0F)F>F)F3F)F)**F(F)F*F))F0F-F)F>F)F)#
\"\"$\"\"%" }}}{EXCHG {PARA 0 "> " 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)*(F(F)&F+6#\"\"#F))&F/6$F5F5F1F)F)*,\"\"'F)F3F)
&F/6$F5F)F)F.F)F7F)F)**\"#=F)F3F)F;F))F7F5F)F)**F1F)F3F)F;F))F.F5F)F)*
*F:F)F3F)&F/6$F)F5F))F;F5F)F)**F>F)F*F)FAF)FCF)F)**F:F)F*F))FCF5F)F;F)
F)**F(F)F*F)F.F)FHF)F)**F:F)F*F)FHF)F7F)F)*,F:F)F*F)FCF)F;F)F.F)F)*,F:
F)F*F)FCF)F7F)F.F)F)**F(F)F3F)FEF)F7F)F)**F1F)F3F)FHF)F;F)F)**F1F)F*F)
FCF)FEF)F)*,F:F)F*F)FCF)F;F)F7F)F)**F1F)F*F)FCF)F?F)F)**F:F)F3F)FEF)F.
F)F)*,F:F)F3F)FCF)F;F)F.F)F)*,F:F)F3F)FCF)F;F)F7F)F)F)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "cond4i:=coeff(coeff(Fi3,D[1,1](f)(
x0,y0)),D[2](f)(x0,y0))=coeff(coeff((1/4)*f3,D[1,1](f)(x0,y0)),D[2](f)
(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4iG/,***\"\"$\"\"
\"&%\"bG6#F)F))&%\"cGF,\"\"#F)&%\"aG6$F)F)F)F)**F(F)F*F)&F26$F)F0F))&F
/6#F0F0F)F)**F(F)&F+F9F)&F26$F0F)F)F-F)F)**F(F)F;F)F7F)&F26$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 11 "" 1 "" {XPPMATH 20 "6#>%'cond
4jG/,2**\"\"'\"\"\"&%\"bG6#F)F)&%\"cGF,F))&%\"aG6$F)F)\"\"#F)F)*,F(F)F
*F)&F16$F)F3F)&F.6#F3F)F0F)F)*,F(F)F*F)F-F)F5F)&F16$F3F)F)F)*,F(F)F*F)
F5F)F7F)&F16$F3F3F)F)**F(F)&F+F8F)F7F))F=F3F)F)*,F(F)F@F)F:F)F-F)F0F)F
)*,F(F)F@F)F5F)F7F)F:F)F)*,F(F)F@F)F:F)F-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$F5F5F1F)F)**F(F)F*F))F.
F5F)&F/6$F)F5F)F)**F(F)F*F))F;F5F)&F/6$F5F)F)F)**F(F)F*F)F;F))F7F5F)F)
*,\"#7F)F*F)F;F)F?F)F.F)F)*,F(F)F*F)F;F)F7F)F.F)F)*,F(F)F*F)F;F)F?F)F7
F)F)*,F(F)F3F)F;F)F?F)F.F)F)*,FDF)F3F)F;F)F?F)F7F)F)**F(F)F3F)F?F)F:F)
F)**F(F)F3F)F;F))F?F5F)F)**F(F)F3F)F?F)FBF)F)*,F(F)F3F)F?F)F.F)F7F)F)#
F)\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 27 "# soluciones para
 el m\351todo" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 160 "metodo:=a
llvalues(solve(\{cond1a,cond2a,cond2b,cond3a,cond3b,cond3c,cond3d,cond
3e,cond4a,cond4b,cond4c,cond4d,cond4f,c[1]=a[1,1]+a[1,2],c[2]=a[2,1]+a
[2,2]\}))[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'metodoG<*/&%\"cG6#
\"\"\",&#F*\"\"#F**&\"\"'!\"\"\"\"$F,F0/&F(6#F-,&F,F**&F/F0F1F,F*/&%\"
aG6$F*F-,&#F*\"\"%F**&F/F0F1F,F0/&F96$F-F*,&F<F**&F/F0F1F,F*/&%\"bGF)F
,/&FFF4F,/&F96$F*F*F</&F96$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<$/%#k2G,$*.\"\"#\"\"\"\"\"$#F+F*%'lambdaG
F+%#y0GF+,&*&F.F+%\"hGF+F+*&F*F+F,F-F+F+,(\"#7F+*(\"\"'F+F.F+F2F+!\"\"
*&)F.F*F+)F2F*F+F+F8F+/%#k1G,$*.F*F+F,F-F.F+F/F+,&*&F*F+F,F-F8F1F+F+F4
F8F8" }}}{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(,(\"
#7F(*(\"\"'F(F+F(F1F(F/*&)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(,(\"#7F(*(\"\"'F(F+F(F/F(!\"\"*&)F+F'F()F/F'F
(F(F5F(" }}}{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(*&,(\"#7\"\"\"*&\"\"'F/9$F/F/*$)F2
\"\"#F/F/F/,(F.F/*&F1F/F2F/!\"\"F3F/F8F(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 
83 "y es f\341cil ver que los complejos con  Re(z)<0  hacen menor el m
\363dulo del numerador " }}{PARA 4 "" 0 "" {TEXT -1 66 "que el del den
ominador, por lo que el m\351todo de GAUSS es A-estable" }}}}{MARK "0 \+
0 0" 6 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }