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{SECT 0 {EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 1 "#" }}{PARA 0 "" 0 "" 
{MPLTEXT 0 21 31 "# inicio del fichero Rkut3e.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 34 "#
 de tres evaluaciones k1, k2 y k3" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 37 
"# Empezaremos con metodos explicitos." }}{PARA 0 "" 0 "" {MPLTEXT 0 
21 7 "# Ahora" }}{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 50 "#      k3:=f(x0+c[3]*h,y0+
a[3,1]*h*k1+a[3,2]*h*k2)" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 14 "# y fina
lmente" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 41 "#      y1:=y0+h*(b[1]*k1+b
[2]*k2+b[3]*k3)" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 7 "# o sea" }}{PARA 
0 "" 0 "" {MPLTEXT 0 21 66 "#      Fi:=b[1]*k1+b[2]*k2+b[3]*k3=Fi_0+h*
Fi10+(h^2/2)*Fi20+O(h^3)" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 14 "# mientr
as que" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 40 "#      De:=Y1+(h/2)*Y2+(h^
2/6)*Y3+O(h^3)" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 36 "# todo esto para e
studiar el orden 3" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 3 "# y" }}{PARA 0 
"" 0 "" {MPLTEXT 0 21 79 "#      Fi:=b[1]*k1+b[2]*k2+b[3]*k3=Fi_0+h*Fi
10+(h^2/2)*Fi20+(h^3/6)*Fi30+O(h^4)" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 
14 "# mientras que" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 52 "#      De:=Y1+
(h/2)*Y2+(h^2/6)*Y3+(h^3/24)*Y4+O(h^4)" }}{PARA 0 "" 0 "" {MPLTEXT 0 
21 29 "# esto para estudiar el error" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 
1 "#" }}}{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 1 0 20 "#y:=unapply(y(x),x):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Y1:=f(x,y(x)):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "Y2:=subs(diff(y(x),x)=Y1,diff(Y1,x)
):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "Y3:=subs(diff(y(x),x)
=Y1,diff(Y2,x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "Y4:=sub
s(diff(y(x),x)=Y1,diff(Y3,x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 39 "Y1:=subs(\{y(x)=y0,x=x0\},Y1):expand(Y1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 39 "Y2:=subs(\{y(x)=y0,x=x0\},Y2):expand(Y2);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,&--&%\"DG6#\"\"\"6#%\"fG6$%#x0G%#y0GF)*&--&
F'6#\"\"#F*F,F)-F+F,F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 
"Y3:=subs(\{y(x)=y0,x=x0\},Y3):expand(Y3);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#,,--&%\"DG6$\"\"\"F)6#%\"fG6$%#x0G%#y0GF)*(\"\"#F)--&F'
6$F)F0F*F,F)-F+F,F)F)*&--&F'6$F0F0F*F,F))F5F0F)F)*&--&F'6#F0F*F,F)--&F
'6#F)F*F,F)F)*&)F=F0F)F5F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 39 "Y4:=subs(\{y(x)=y0,x=x0\},Y4):expand(Y4);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#,8--&%\"DG6%\"\"\"F)F)6#%\"fG6$%#x0G%#y0GF)*(\"\"$F)--&
F'6%F)F)\"\"#F*F,F)-F+F,F)F)*(F0F)--&F'6%F)F5F5F*F,F))F6F5F)F)*(F0F)--
&F'6$F)F5F*F,F)--&F'6#F)F*F,F)F)**\"\"&F)F>F)--&F'6#F5F*F,F)F6F)F)*&--
&F'6%F5F5F5F*F,F))F6F0F)F)**F0F)F6F)--&F'6$F5F5F*F,F)FBF)F)**\"\"%F)FS
F)FHF)F<F)F)*&FHF)--&F'6$F)F)F*F,F)F)*&)FHF5F)FBF)F)*&)FHF0F)F6F)F)" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "k1_:=f(x0,y0):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "k2_:=f(x0+c[2]*h,y0+a[2,1]*h*k1_):
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "k3_:=f(x0+c[3]*h,y0+a[3
,1]*h*k1_+a[3,2]*h*k2_):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 
"k1_0:=subs(h=0,k1_):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k2
_0:=subs(h=0,k2_):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k3_0:
=subs(h=0,k3_):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k11:=dif
f(k1_,h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k21:=diff(k2_,
h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k31:=diff(k3_,h);" }
}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$k31G,&*&--&%\"DG6#\"\"\"6#%\"fG6$,
&%#x0GF,*&&%\"cG6#\"\"$F,%\"hGF,F,,(%#y0GF,*(&%\"aG6$F6F,F,F7F,-F.6$F1
F9F,F,*(&F<6$F6\"\"#F,F7F,-F.6$,&F1F,*&&F46#FCF,F7F,F,,&F9F,*(&F<6$FCF
,F,F7F,F>F,F,F,F,F,F3F,F,*&--&F*FIF-F/F,,(*&F;F,F>F,F,*&FAF,FDF,F,*(FA
F,F7F,,&*&-F(FEF,FHF,F,*(-FPFEF,FLF,F>F,F,F,F,F,F," }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 20 "k110:=subs(h=0,k11):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 20 "k210:=subs(h=0,k21):" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 20 "k310:=subs(h=0,k31):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 17 "k12:=diff(k11,h):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "k22:=diff(k21,h):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "k32:=diff(k31,h);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#
>%$k32G,(*&,&*&--&%\"DG6$\"\"\"F.6#%\"fG6$,&%#x0GF.*&&%\"cG6#\"\"$F.%
\"hGF.F.,(%#y0GF.*(&%\"aG6$F8F.F.F9F.-F06$F3F;F.F.*(&F>6$F8\"\"#F.F9F.
-F06$,&F3F.*&&F66#FEF.F9F.F.,&F;F.*(&F>6$FEF.F.F9F.F@F.F.F.F.F.F5F.F.*
&--&F,6$F.FEF/F1F.,(*&F=F.F@F.F.*&FCF.FFF.F.*(FCF.F9F.,&*&--&F,6#F.F/F
GF.FJF.F.*(--&F,FKF/FGF.FNF.F@F.F.F.F.F.F.F.F5F.F.*&,&*&FQF.F5F.F.*&--
&F,6$FEFEF/F1F.FUF.F.F.FUF.F.*&-F[oF1F.,&*(FEF.FCF.FYF.F.*(FCF.F9F.,&*
&,&*&-F*FGF.FJF.F.*(-FRFGF.FNF.F@F.F.F.FJF.F.*(,&*&F`pF.FJF.F.*(-FboFG
F.FNF.F@F.F.F.FNF.F@F.F.F.F.F.F." }}}{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 20 "k320:=subs(h=0,k32);" }}{PARA 12 "" 1 "" {XPPMATH 20 
"6#>%%k320G,(*&,&*&--&%\"DG6$\"\"\"F.6#%\"fG6$%#x0G%#y0GF.&%\"cG6#\"\"
$F.F.*&--&F,6$F.\"\"#F/F1F.,&*&&%\"aG6$F7F.F.-F0F1F.F.*&&FA6$F7F=F.FCF
.F.F.F.F.F4F.F.*&,&*&F9F.F4F.F.*&--&F,6$F=F=F/F1F.F>F.F.F.F>F.F.**F=F.
--&F,6#F=F/F1F.FEF.,&*&--&F,6#F.F/F1F.&F5FSF.F.*(FPF.&FA6$F=F.F.FCF.F.
F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k13:=diff(k12,h):" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k23:=diff(k22,h):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k33:=diff(k32,h);" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#>%$k33G,**&,(*&,&*&--&%\"DG6%\"\"\"F0F06#%\"
fG6$,&%#x0GF0*&&%\"cG6#\"\"$F0%\"hGF0F0,(%#y0GF0*(&%\"aG6$F:F0F0F;F0-F
26$F5F=F0F0*(&F@6$F:\"\"#F0F;F0-F26$,&F5F0*&&F86#FGF0F;F0F0,&F=F0*(&F@
6$FGF0F0F;F0FBF0F0F0F0F0F7F0F0*&--&F.6%F0F0FGF1F3F0,(*&F?F0FBF0F0*&FEF
0FHF0F0*(FEF0F;F0,&*&--&F.6#F0F1FIF0FLF0F0*(--&F.FMF1FIF0FPF0FBF0F0F0F
0F0F0F0F7F0F0*&,&*&FSF0F7F0F0*&--&F.6%F0FGFGF1F3F0FWF0F0F0FWF0F0*&--&F
.6$F0FGF1F3F0,&*(FGF0FEF0FenF0F0*(FEF0F;F0,&*&,&*&--&F.6$F0F0F1FIF0FLF
0F0*(-FioFIF0FPF0FBF0F0F0FLF0F0*(,&*&FhpF0FLF0F0*(--&F.6$FGFGF1FIF0FPF
0FBF0F0F0FPF0FBF0F0F0F0F0F0F0F7F0F0*&,(*&F`oF0F7F0F0*&,&*&FcoF0F7F0F0*
&--&F.6%FGFGFGF1F3F0FWF0F0F0FWF0F0*&-F^qF3F0F\\pF0F0F0FWF0F0*(FGF0,&*&
FhoF0F7F0F0*&F]rF0FWF0F0F0F\\pF0F0*&-F]oF3F0,&*(F:F0FEF0F_pF0F0*(FEF0F
;F0,&*&,&*&,&*&-F,FIF0FLF0F0*(-FTFIF0FPF0FBF0F0F0FLF0F0*(,&*&F_sF0FLF0
F0*(-FdoFIF0FPF0FBF0F0F0FPF0FBF0F0F0FLF0F0*(,&*&FasF0FLF0F0*(,&*&FdsF0
FLF0F0*(-FiqFIF0FPF0FBF0F0F0FPF0FBF0F0F0FPF0FBF0F0F0F0F0F0" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k130:=subs(h=0,k13):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k230:=subs(h=0,k23):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k330:=subs(h=0,k33);" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#>%%k330G,**&,(*&,&*&--&%\"DG6%\"\"\"F0F06#%\"fG6
$%#x0G%#y0GF0&%\"cG6#\"\"$F0F0*&--&F.6%F0F0\"\"#F1F3F0,&*&&%\"aG6$F9F0
F0-F2F3F0F0*&&FC6$F9F?F0FEF0F0F0F0F0F6F0F0*&,&*&F;F0F6F0F0*&--&F.6%F0F
?F?F1F3F0F@F0F0F0F@F0F0**F?F0--&F.6$F0F?F1F3F0FGF0,&*&--&F.6#F0F1F3F0&
F76#F?F0F0*(--&F.FgnF1F3F0&FC6$F?F0F0FEF0F0F0F0F0F6F0F0*&,(*&FJF0F6F0F
0*&,&*&FMF0F6F0F0*&--&F.6%F?F?F?F1F3F0F@F0F0F0F@F0F0**F?F0--&F.6$F?F?F
1F3F0FGF0FVF0F0F0F@F0F0**\"\"%F0,&*&FRF0F6F0F0*&FjoF0F@F0F0F0FGF0FVF0F
0**F9F0FinF0FGF0,&*&,&*&--&F.6$F0F0F1F3F0FfnF0F0*(FRF0F\\oF0FEF0F0F0Ff
nF0F0*(,&*&FRF0FfnF0F0*(FjoF0F\\oF0FEF0F0F0F\\oF0FEF0F0F0F0" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "Fi_0:=expand(b[1]*k1_0+b[2]*
k2_0+b[3]*k3_0):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "Fi10:=e
xpand(b[1]*k110+b[2]*k210+b[3]*k310):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 44 "Fi20:=expand(b[1]*k120+b[2]*k220+b[3]*k320):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "Fi30:=expand(b[1]*k130+b[2]*
k230+b[3]*k330):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# condic
iones para el orden 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "co
nd1a:=coeff(Y1,f(x0,y0))=coeff(Fi_0,f(x0,y0));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%'cond1aG/\"\"\",(&%\"bG6#F&F&&F)6#\"\"#F&&F)6#\"\"$F&
" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# condiciones para el or
den 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "cond2a:=(1/2)*coef
f(Y2,D[1](f)(x0,y0))=coeff(Fi10,D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%'cond2aG/#\"\"\"\"\"#,&*&&%\"bG6#F(F'&%\"cGF-F'F'*&&F
,6#\"\"$F'&F/F2F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "cond
2b:=(1/2)*coeff(coeff(Y2,D[2](f)(x0,y0)),f(x0,y0))=coeff(coeff(Fi10,D[
2](f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2bG
/#\"\"\"\"\"#,(*&&%\"bG6#F(F'&%\"aG6$F(F'F'F'*&&F,6#\"\"$F'&F/6$F4F'F'
F'*&F2F'&F/6$F4F(F'F'" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# c
ondiciones para el orden 3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
70 "cond3a:=(1/3)*coeff(Y3,D[1,1](f)(x0,y0))=coeff(Fi20,D[1,1](f)(x0,y
0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3aG/#\"\"\"\"\"$,&*&&%
\"bG6#\"\"#F')&%\"cGF-F.F'F'*&&F,6#F(F')&F1F4F.F'F'" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 102 "cond3b:=(1/3)*coeff(coeff(Y3,D[1,2](f)(x
0,y0)),f(x0,y0))=coeff(coeff(Fi20,D[1,2](f)(x0,y0)),f(x0,y0));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3bG/#\"\"#\"\"$,(**F'\"\"\"&%\"
bG6#F'F+&%\"cGF.F+&%\"aG6$F'F+F+F+**F'F+&F-6#F(F+&F0F6F+&F26$F(F+F+F+*
*F'F+F5F+F7F+&F26$F(F'F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
106 "cond3c:=(1/3)*coeff(coeff(Y3,D[2,2](f)(x0,y0)),f(x0,y0)^2)=coeff(
coeff(Fi20,D[2,2](f)(x0,y0)),f(x0,y0)^2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%'cond3cG/#\"\"\"\"\"$,**&&%\"bG6#\"\"#F')&%\"aG6$F.F'
F.F'F'*&&F,6#F(F')&F16$F(F'F.F'F'**F.F'F4F'F7F'&F16$F(F.F'F'*&F4F')F:F
.F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "cond3d:=(1/3)*coe
ff(coeff(Y3,D[2](f)(x0,y0)),D[1](f)(x0,y0))=coeff(coeff(Fi20,D[2](f)(x
0,y0)),D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3dG/
#\"\"\"\"\"$,$**\"\"#F'&%\"bG6#F(F'&%\"aG6$F(F+F'&%\"cG6#F+F'F'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "cond3e:=(1/3)*coeff(coeff(Y
3,D[2](f)(x0,y0)^2),f(x0,y0))=coeff(coeff(Fi20,D[2](f)(x0,y0)^2),f(x0,
y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3eG/#\"\"\"\"\"$,$**\"
\"#F'&%\"bG6#F(F'&%\"aG6$F(F+F'&F06$F+F'F'F'" }}}{EXCHG {PARA 0 "" 0 "
" {MPLTEXT 0 21 29 "# condiciones para el orden 4" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 74 "cond4a:=(1/4)*coeff(Y4,D[1,1,1](f)(x0,y0))=c
oeff(Fi30,D[1,1,1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'c
ond4aG/#\"\"\"\"\"%,&*&&%\"bG6#\"\"#F')&%\"cGF-\"\"$F'F'*&&F,6#F2F')&F
1F5F2F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "cond4b:=(1/4)
*coeff(coeff(Y4,D[1,1,2](f)(x0,y0)),f(x0,y0))=coeff(coeff(Fi30,D[1,1,2
](f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4bG/
#\"\"$\"\"%,(**F'\"\"\"&%\"bG6#\"\"#F+)&%\"cGF.F/F+&%\"aG6$F/F+F+F+**F
'F+&F-6#F'F+)&F2F8F/F+&F46$F'F+F+F+**F'F+F7F+F9F+&F46$F'F/F+F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "cond4c:=(1/4)*coeff(coeff(Y
4,D[1,2,2](f)(x0,y0)),f(x0,y0)^2)=coeff(coeff(Fi30,D[1,2,2](f)(x0,y0))
,f(x0,y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4cG/#\"\"$\"\"
%,***F'\"\"\"&%\"bG6#\"\"#F+&%\"cGF.F+)&%\"aG6$F/F+F/F+F+*,\"\"'F+&F-6
#F'F+&F1F9F+&F46$F'F+F+&F46$F'F/F+F+**F'F+F8F+F:F+)F;F/F+F+**F'F+F8F+F
:F+)F=F/F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 114 "cond4d:=(1
/4)*coeff(coeff(Y4,D[1,2](f)(x0,y0)),D[1](f)(x0,y0))=coeff(coeff(Fi30,
D[1,2](f)(x0,y0)),D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%'cond4dG/#\"\"$\"\"%,$*,\"\"'\"\"\"&%\"bG6#F'F,&%\"cGF/F,&%\"aG6$F'
\"\"#F,&F16#F5F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 146 "cond
4e:=(1/4)*coeff(coeff(coeff(Y4,D[1,2](f)(x0,y0)),D[2](f)(x0,y0)),f(x0,
y0))=coeff(coeff(coeff(Fi30,D[1,2](f)(x0,y0)),D[2](f)(x0,y0)),f(x0,y0)
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4eG/#\"\"&\"\"%,&*,\"\"'
\"\"\"&%\"bG6#\"\"$F,&%\"aG6$F0\"\"#F,&%\"cG6#F4F,&F26$F4F,F,F,*,F+F,F
-F,&F6F/F,F1F,F8F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "co
nd4f:=(1/4)*coeff(coeff(Y4,D[2,2,2](f)(x0,y0)),f(x0,y0)^3)=coeff(coeff
(Fi30,D[2,2,2](f)(x0,y0)),f(x0,y0)^3);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%'cond4fG/#\"\"\"\"\"%,,*&&%\"bG6#\"\"#F')&%\"aG6$F.F'\"\"$F'F'
*&&F,6#F3F')&F16$F3F'F3F'F'*&F5F')&F16$F3F.F3F'F'**F3F'F5F'F8F')F<F.F'
F'**F3F'F5F')F8F.F'F<F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
146 "cond4g:=(1/4)*coeff(coeff(coeff(Y4,D[2,2](f)(x0,y0)),D[1](f)(x0,y
0)),f(x0,y0))=coeff(coeff(coeff(Fi30,D[2,2](f)(x0,y0)),D[1](f)(x0,y0))
,f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4gG/#\"\"$\"\"%,
&*,\"\"'\"\"\"&%\"bG6#F'F,&%\"aG6$F'\"\"#F,&%\"cG6#F3F,&F16$F'F,F,F,**
F+F,F-F,)F0F3F,F4F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 150 "c
ond4h:=(1/4)*coeff(coeff(coeff(Y4,D[2,2](f)(x0,y0)),D[2](f)(x0,y0)),f(
x0,y0)^2)=coeff(coeff(coeff(Fi30,D[2,2](f)(x0,y0)),D[2](f)(x0,y0)),f(x
0,y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4hG/\"\"\",(*,\"\"
'F&&%\"bG6#\"\"$F&&%\"aG6$F-\"\"#F&&F/6$F1F&F&&F/6$F-F&F&F&**F)F&F*F&)
F.F1F&F2F&F&**F-F&F*F&F.F&)F2F1F&F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 114 "cond4i:=(1/4)*coeff(coeff(Y4,D[1,1](f)(x0,y0)),D[2](
f)(x0,y0))=coeff(coeff(Fi30,D[1,1](f)(x0,y0)),D[2](f)(x0,y0));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4iG/#\"\"\"\"\"%,$**\"\"$F'&%\"
bG6#F+F'&%\"aG6$F+\"\"#F')&%\"cG6#F2F2F'F'" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 114 "cond4j:=(1/4)*coeff(coeff(Y4,D[1](f)(x0,y0)),D[2](
f)(x0,y0)^2)=coeff(coeff(Fi30,D[1](f)(x0,y0)),D[2](f)(x0,y0)^2);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4jG/#\"\"\"\"\"%\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "cond4k:=(1/4)*coeff(coeff(Y
4,D[2](f)(x0,y0)^3),f(x0,y0))=coeff(coeff(Fi30,D[2](f)(x0,y0)^3),f(x0,
y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond4kG/#\"\"\"\"\"%\"\"!
" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 28 "# soluciones para el ord
en 3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "con1ecua:=\{cond1a,
cond2a,cond2b,cond3a,cond3b,cond3c,cond3d,cond3e\}:" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 65 "solucion1:=solve(con1ecua,\{c[2],a[2,1],a
[3,1],a[3,2],b[1],b[2]\});" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*soluc
ion1G<(/&%\"cG6#\"\"#,$*&#F*\"\"$\"\"\"*&,&F/!\"\"*(F.F/&%\"bG6#F.F/)&
F(F6F*F/F/F/,&F/F2*(F*F/F4F/F8F/F/F2F/F//&F56#F/,$*&#F/\"\"%F/*&,*F/F2
*(\"#7F/F4F/F7F/F/*(FEF/F4F/F8F/F2*&FAF/F4F/F/F/F1F2F/F//&F5F),$*&#F.F
AF/*&F9F*F1F2F/F2/&%\"aG6$F*F/F+/&FP6$F.F/,$*&F@F/*(,(*(\"\"'F/F4F/F8F
/F2*(FEF/)F4F*F/)F8F.F/F/F/F/F/F4F2F1F2F/F//&FP6$F.F*,$*&F@F/*(F4F2F1F
2F9F/F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "e2:=solve(-1+2
*b[3]*c[3],\{b[3]\});con2ecua:=subs(e2,con1ecua):solucion2:=solve(con2
ecua union e2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e2G<#/&%\"bG6#\"
\"$,$*&#\"\"\"\"\"#F.*&F.F.&%\"cGF)!\"\"F.F." }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%*solucion2G<*/&%\"cG6#\"\"#F'/&F(6#\"\"$#F*F./&%\"bG6
#\"\"\"#F4\"\"%/&F2F)\"\"!/&F2F-#F.F6/&%\"aG6$F*F4F'/&F?6$F.F4,$*&#F*
\"\"*F4*&,&*&F.F4F'F4F4F4!\"\"F4F'FKF4F4/&F?6$F.F*,$*&FFF4*&F4F4F'FKF4
F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "e3:=solve(-1+3*b[3]*c
[3]^2,\{b[3]\});con3ecua:=subs(e3,con1ecua):solucion3:=solve(con3ecua \+
union e3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e3G<#/&%\"bG6#\"\"$,$
*&#\"\"\"F*F.*&F.F.*$)&%\"cGF)\"\"#F.!\"\"F.F." }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%*solucion3G<*/&%\"cG6#\"\"$#\"\"#F*/&%\"bG6#\"\"\"#F1
\"\"%/&F/6#F,\"\"!/&F/F)#F*F3/&%\"aG6$F*F,F</&F(F6,$*&#F,\"\"*F1*&F1F1
F<!\"\"F1F1/&F=6$F,F1FA/&F=6$F*F1,&F+F1F<FF" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 34 "#latex(solucion3,\"solucion3.txt\");" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "e4:=solve(b[3],\{b[3]\});con4ecua:=
subs(e4,con1ecua):solucion4:=solve(con4ecua union e4);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%#e4G<#/&%\"bG6#\"\"$\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%*solucion4G6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 83 "simplify(subs(solucion1,c[2]-a[2,1]));simplify(subs(solucion1,
c[3]-a[3,1]-a[3,2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 83 "simplify(subs(solucion2,c[2]-a[2,1]));simplify(subs(s
olucion2,c[3]-a[3,1]-a[3,2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"
!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 83 "simplify(subs(solucion3,c[2]-a[2,1]));simplify(subs
(solucion3,c[3]-a[3,1]-a[3,2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"
\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 83 "simplify(subs(solucion4,c[2]-a[2,1]));simplify(s
ubs(solucion4,c[3]-a[3,1]-a[3,2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#,&&%\"cG6#\"\"#\"\"\"&%\"aG6$F'F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,(&%\"cG6#\"\"$\"\"\"&%\"aG6$F'F(!\"\"&F*6$F'\"\"#F," }}}{EXCHG 
{PARA 0 "" 0 "" {MPLTEXT 0 21 28 "# coeficientes para el error" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "tau4a:=(1/4)*coeff(Y4,D[1,1,
1](f)(x0,y0))-coeff(Fi30,D[1,1,1](f)(x0,y0));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&tau4aG,(#\"\"\"\"\"%F'*&&%\"bG6#\"\"#F')&%\"cGF,\"\"
$F'!\"\"*&&F+6#F1F')&F0F5F1F'F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 105 "tau4b:=(1/4)*coeff(coeff(Y4,D[1,1,2](f)(x0,y0)),f(x0,y0))-coe
ff(coeff(Fi30,D[1,1,2](f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&tau4bG,*#\"\"$\"\"%\"\"\"**F'F)&%\"bG6#\"\"#F))&%\"c
GF-F.F)&%\"aG6$F.F)F)!\"\"**F'F)&F,6#F'F))&F1F8F.F)&F36$F'F)F)F5**F'F)
F7F)F9F)&F36$F'F.F)F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "t
au4c:=(1/4)*coeff(coeff(Y4,D[1,2,2](f)(x0,y0)),f(x0,y0)^2)-coeff(coeff
(Fi30,D[1,2,2](f)(x0,y0)),f(x0,y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%&tau4cG,,#\"\"$\"\"%\"\"\"**F'F)&%\"bG6#\"\"#F)&%\"cGF-F))&%\"
aG6$F.F)F.F)!\"\"*,\"\"'F)&F,6#F'F)&F0F9F)&F36$F'F)F)&F36$F'F.F)F5**F'
F)F8F)F:F))F;F.F)F5**F'F)F8F)F:F))F=F.F)F5" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 113 "tau4d:=(1/4)*coeff(coeff(Y4,D[1,2](f)(x0,y0)),D[1]
(f)(x0,y0))-coeff(coeff(Fi30,D[1,2](f)(x0,y0)),D[1](f)(x0,y0));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&tau4dG,&#\"\"$\"\"%\"\"\"*,\"\"'F)&
%\"bG6#F'F)&%\"cGF.F)&%\"aG6$F'\"\"#F)&F06#F4F)!\"\"" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 145 "tau4e:=(1/4)*coeff(coeff(coeff(Y4,D[1,2]
(f)(x0,y0)),D[2](f)(x0,y0)),f(x0,y0))-coeff(coeff(coeff(Fi30,D[1,2](f)
(x0,y0)),D[2](f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%&tau4eG,(#\"\"&\"\"%\"\"\"*,\"\"'F)&%\"bG6#\"\"$F)&%\"aG6$F/\"\"#F)
&%\"cG6#F3F)&F16$F3F)F)!\"\"*,F+F)F,F)&F5F.F)F0F)F7F)F9" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "tau4f:=(1/4)*coeff(coeff(Y4,D[2,2,
2](f)(x0,y0)),f(x0,y0)^3)-coeff(coeff(Fi30,D[2,2,2](f)(x0,y0)),f(x0,y0
)^3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&tau4fG,.#\"\"\"\"\"%F'*&&%
\"bG6#\"\"#F')&%\"aG6$F-F'\"\"$F'!\"\"*&&F+6#F2F')&F06$F2F'F2F'F3*&F5F
')&F06$F2F-F2F'F3**F2F'F5F'F8F')F<F-F'F3**F2F'F5F')F8F-F'F<F'F3" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 145 "tau4g:=(1/4)*coeff(coeff(co
eff(Y4,D[2,2](f)(x0,y0)),D[1](f)(x0,y0)),f(x0,y0))-coeff(coeff(coeff(F
i30,D[2,2](f)(x0,y0)),D[1](f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&tau4gG,(#\"\"$\"\"%\"\"\"*,\"\"'F)&%\"bG6#F'F)&%\"aG
6$F'\"\"#F)&%\"cG6#F2F)&F06$F'F)F)!\"\"**F+F)F,F))F/F2F)F3F)F8" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "tau4h:=(1/4)*coeff(coeff(co
eff(Y4,D[2,2](f)(x0,y0)),D[2](f)(x0,y0)),f(x0,y0)^2)-coeff(coeff(coeff
(Fi30,D[2,2](f)(x0,y0)),D[2](f)(x0,y0)),f(x0,y0)^2);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%&tau4hG,*\"\"\"F&*,\"\"'F&&%\"bG6#\"\"$F&&%\"aG6$F
,\"\"#F&&F.6$F0F&F&&F.6$F,F&F&!\"\"**F(F&F)F&)F-F0F&F1F&F5**F,F&F)F&F-
F&)F1F0F&F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "tau4i:=(1/4
)*coeff(coeff(Y4,D[1,1](f)(x0,y0)),D[2](f)(x0,y0))-coeff(coeff(Fi30,D[
1,1](f)(x0,y0)),D[2](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
&tau4iG,&#\"\"\"\"\"%F'**\"\"$F'&%\"bG6#F*F'&%\"aG6$F*\"\"#F')&%\"cG6#
F1F1F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "tau4j:=(1/4
)*coeff(coeff(Y4,D[1](f)(x0,y0)),D[2](f)(x0,y0)^2)-coeff(coeff(Fi30,D[
1](f)(x0,y0)),D[2](f)(x0,y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
&tau4jG#\"\"\"\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "tau
4k:=(1/4)*coeff(coeff(Y4,D[2](f)(x0,y0)^3),f(x0,y0))-coeff(coeff(Fi30,
D[2](f)(x0,y0)^3),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&tau
4kG#\"\"\"\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 62 "# llamada
 al paquete 'Optimization' para 'Minimize' (numerico)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "with(Optimization):" }}}{EXCHG 
{PARA 0 "" 0 "" {MPLTEXT 0 21 71 "# como queda lo del error para los m
etodos de orden 3 (primera familia)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 151 "Norma2tau_alcuadrado_primerafamilia:=simplify(subs(s
olucion1,tau4a^2+tau4b^2+tau4c^2+tau4d^2+tau4e^2+tau4f^2+tau4g^2+tau4h
^2+tau4i^2+tau4j^2+tau4k^2));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%DNo
rma2tau_alcuadrado_primerafamiliaG,$*&#\"\"\"\"$['F(*&,8*(\"&gH\"F()&%
\"bG6#\"\"$\"\"#F()&%\"cGF1\"\"'F(F(*(\"&gX$F()F5\"\"&F(F.F(!\"\"*(\"&
K!eF(F.F()F5\"\"%F(F(*(\"&Sk%F(F.F()F5F2F(F<*(\"&w\\\"F(F/F(FCF(F<*(\"
&%G8F(F.F()F5F3F(F(*(\"&w+#F(F/F(FHF(F(*&\"%#f#F(FHF(F(*(\"%krF(F/F(F5
F(F<*&\"%kNF(F5F(F<\"%L8F(F(,&F(F<*(F3F(F/F(F5F(F(!\"#F(F(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "Norma2tau_alcuadrado_primerafamilia
_c334:=subs(\{c[3]=3/4\},Norma2tau_alcuadrado_primerafamilia);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%INorma2tau_alcuadrado_primerafamilia
_c334G,$*&#\"\"\"\"$['F(*&,(*&#\"&pW%\"$G\"F(*$)&%\"bG6#\"\"$\"\"#F(F(
F(*&#\"%$f\"\"\"%F(F2F(!\"\"\"$=\"F(F(,&F(F;*&#F5F6F(F2F(F(!\"#F(F(" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "min1_primerafamilia:=Minim
ize(Norma2tau_alcuadrado_primerafamilia);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%4min1_primerafamiliaG7$$\"3qfIRl7ZB8!#=7$/&%\"cG6#\"
\"$$\"3&zEd5&f26xF(/&%\"bGF-$\"3%=!fF9IieUF(" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 127 "min_primerafamilia:=minimize(Norma2tau_alcuadra
do_primerafamilia,location=true);minf_primerafamilia:=evalf(min_primer
afamilia);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%3min_primerafamiliaG6$
-%)minimizeG6$,$*&#\"\"\"\"$['F,*&,8*(\"&gH\"F,)&%\"bG6#\"\"$\"\"#F,)&
%\"cGF5\"\"'F,F,*(\"&gX$F,)F9\"\"&F,F2F,!\"\"*(\"&K!eF,F2F,)F9\"\"%F,F
,*(\"&Sk%F,F2F,)F9F6F,F@*(\"&w\\\"F,F3F,FGF,F@*(\"&%G8F,F2F,)F9F7F,F,*
(\"&w+#F,F3F,FLF,F,*&\"%#f#F,FLF,F,*(\"%krF,F3F,F9F,F@*&\"%kNF,F9F,F@
\"%L8F,F,,&F,F@*(F7F,F3F,F9F,F,!\"#F,F,/%)locationG%%trueG<\"" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%4minf_primerafamiliaG6%-%)minimizeG6
$,$*&#\"\"\"\"$['F,*&,8*(\"&gH\"F,)&%\"bG6#\"\"$\"\"#F,)&%\"cGF5\"\"'F
,F,*(\"&gX$F,)F9\"\"&F,F2F,!\"\"*(\"&K!eF,F2F,)F9\"\"%F,F,*(\"&Sk%F,F2
F,)F9F6F,F@*(\"&w\\\"F,F3F,FGF,F@*(\"&%G8F,F2F,)F9F7F,F,*(\"&w+#F,F3F,
FLF,F,*&\"%#f#F,FLF,F,*(\"%krF,F3F,F9F,F@*&\"%kNF,F9F,F@\"%L8F,F,,&F,F
@*(F7F,F3F,F9F,F,!\"#F,F,/%)locationG%%trueG<\"Ffn" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 132 "min_primerafamilia:=minimize(Norma2tau_alc
uadrado_primerafamilia_c334,location=true);minf_primerafamilia:=evalf(
min_primerafamilia);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%3min_primera
familiaG6$#\"#f\"$U%<#7$<#/&%\"bG6#\"\"$#\"$W*\"%z?F&" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%4minf_primerafamiliaG6$$\"+H;%[L\"!#5<#7$<#/&%\"
bG6#\"\"$$\"+TXkSXF(F&" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 71 "# \+
como queda lo del error para los metodos de orden 3 (segunda familia)
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 151 "Norma2tau_alcuadrado_s
egundafamilia:=simplify(subs(solucion2,tau4a^2+tau4b^2+tau4c^2+tau4d^2
+tau4e^2+tau4f^2+tau4g^2+tau4h^2+tau4i^2+tau4j^2+tau4k^2));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%DNorma2tau_alcuadrado_segundafamiliaG,(#\"
$L%\"$['\"\"\"*&#\"\"(\"\"%F)&%\"cG6#\"\"#F)!\"\"*&#\"\"$F1F)*$)F.F1F)
F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 127 "min_segundafamilia
:=minimize(Norma2tau_alcuadrado_segundafamilia,location=true);minf_seg
undafamilia:=evalf(min_segundafamilia);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%3min_segundafamiliaG6$#\"$4%\"%#f#<#7$<#/&%\"cG6#\"\"##\"\"(\"
#7F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%4minf_segundafamiliaG6$$\"+*
4Kzd\"!#5<#7$<#/&%\"cG6#\"\"#$\"+LLLLeF(F&" }}}{EXCHG {PARA 0 "" 0 "" 
{MPLTEXT 0 21 71 "# como queda lo del error para los metodos de orden \+
3 (tercera familia)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 151 "Nor
ma2tau_alcuadrado_tercerafamilia:=simplify(subs(solucion3,tau4a^2+tau4
b^2+tau4c^2+tau4d^2+tau4e^2+tau4f^2+tau4g^2+tau4h^2+tau4i^2+tau4j^2+ta
u4k^2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%DNorma2tau_alcuadrado_te
rcerafamiliaG,$*&#\"\"\"\"$['F(*&,(*&\"$L%F()&%\"aG6$\"\"$\"\"#F3F(F(*
&\"$_#F(F/F(!\"\"\"#[F(F(F/!\"#F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 127 "min_tercerafamilia:=minimize(Norma2tau_alcuadrado_te
rcerafamilia,location=true);minf_tercerafamilia:=evalf(min_tercerafami
lia);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%3min_tercerafamiliaG6$#\"$4
%\"%#f#<#7$<#/&%\"aG6$\"\"$\"\"##\"\")\"#@F&" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%4minf_tercerafamiliaG6$$\"+*4Kzd\"!#5<#7$<#/&%\"aG6$
\"\"$\"\"#$\"+5Q_4QF(F&" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 74 "#
 como queda lo del error para lel metodo de error minimo dado por Dorm
and" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "metodoDormand1:=\{c[
2]=1/2,c[3]=3/4,a[2,1]=1/2,a[3,1]=0,a[3,2]=3/4,b[1]=2/9,b[2]=1/3,b[3]=
4/9\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 289 "Norma2tau_alcuad
rado_primerafamilia_metodoDormand1:=subs(metodoDormand1,Norma2tau_alcu
adrado_primerafamilia):min_primerafamilia_metodoDormand1:=Norma2tau_al
cuadrado_primerafamilia_metodoDormand1;minf_primerafamilia_metodoDorma
nd1:=evalf(Norma2tau_alcuadrado_primerafamilia_metodoDormand1);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%Bmin_primerafamilia_metodoDormand1G#
\"#x\"$w&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%Cminf_primerafamilia_me
todoDormand1G$\"+cb!oL\"!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
"" }}}}{MARK "0 1 0" 31 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }