{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 "" -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 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 1 18 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 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 270 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 271 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 272 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 273 "" 1 24 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 }} {SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 271 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 273 22 "(8) Estabilidad lineal" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 272 16 "Ejercicio 08-01 " }} {PARA 4 "" 0 "" {TEXT -1 79 "\na) Cu\341l es el mayor orden posible qu e puede alcanzar un m\351todo de Runge-Kutta " }}{PARA 4 "" 0 "" {TEXT -1 24 "con el siguiente tablero" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 4 "" 0 "" {TEXT 256 19 " 0 | " }}{PARA 4 "" 0 "" {TEXT 257 9 " 1/(2 " }{XPPEDIT 18 0 "alpha" "6#%&alphaG" }{TEXT 265 15 ") | 1/(2 " }{XPPEDIT 18 0 "alpha" "6#%&alphaG" }{TEXT 266 1 ")" }}{PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 258 24 " ------------------------" }}{PARA 4 "" 0 "" {TEXT 259 31 " \+ | 1 - " }{XPPEDIT 18 0 "alpha" "6#%&alphaG" }{TEXT 267 7 " " }{XPPEDIT 18 0 "alpha" "6#%&alphaG" }{TEXT 268 1 " " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 46 "(lo que a ntecede es Ejercicio del cap\355tulo 3)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 9 "b) Para " }{TEXT 269 1 " " } {XPPEDIT 18 0 "alpha" "6#%&alphaG" }{TEXT -1 67 " arbitrario, calc \372lese la funci\363n de estabilidad de estos m\351todos" }}}{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 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 28 "Y1:=subs(\{y(x)=y0,x= x0\},y1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y2:=subs(\{y(x )=y0,x=x0\},y2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y3:=sub s(\{y(x)=y0,x=x0\},y3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 " k1_:=f(x0,y0):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "k2_:=f(x0 +1/(2*alpha)*h,y0+1/(2*alpha)*h*k1_):" }}}{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 17 "k11:=diff(k1_,h):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k21:=diff(k2_,h):" }}}{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 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):" }}}{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):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 263 2 "a)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 27 "condiciones p ara el orden 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Fi_0:=exp and((1-alpha)*k1_0+alpha*k2_0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%% Fi_0G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 " cond1a:=coeff(Y1,f(x0,y0))=coeff(Fi_0,f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond1aG/\"\"\"F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 261 27 "condiciones para el orden 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Fi10:=expand((1-alpha)*k110+alpha*k210);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi10G,&*&#\"\"\"\"\"#F(--&%\"DG6#F(6#%\"fG6$ %#x0G%#y0GF(F(*&F'F(*&--&F-6#F)F/F1F(-F0F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "cond2a:=(1/2)*coeff(Y2,D[1](f)(x0,y0))=coeff( Fi10,D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2aG/# \"\"\"\"\"#F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "cond2b:=(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/#\"\" \"\"\"#F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 262 28 "condiciones para el orden 3 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Fi20:=expand(( 1-alpha)*k120+alpha*k220);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi20G ,(*&#\"\"\"\"\"%F(*&--&%\"DG6$F(F(6#%\"fG6$%#x0G%#y0GF(%&alphaG!\"\"F( F(*&#F(\"\"#F(*(--&F.6$F(F9F0F2F(F5F6-F1F2F(F(F(*&F'F(*(F5F6F?F9--&F.6 $F9F9F0F2F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "cond3a:= (1/6)*coeff(Y3,D[1,1](f)(x0,y0))=(1/2)*coeff(Fi20,D[1,1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3aG/#\"\"\"\"\"',$*&F'F'*&\" \")F'%&alphaGF'!\"\"F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 " cond3b:=(1/6)*coeff(coeff(Y3,D[1,2](f)(x0,y0)),f(x0,y0))=(1/2)*coeff(c oeff(Fi20,D[1,2](f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3bG/#\"\"\"\"\"$,$*&F'F'*&\"\"%F'%&alphaGF'!\"\"F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "cond3c:=(1/6)*coeff(coeff(Y 3,D[2,2](f)(x0,y0)),f(x0,y0)^2)=(1/2)*coeff(coeff(Fi20,D[2,2](f)(x0,y0 )),f(x0,y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3cG/#\"\"\" \"\"',$*&F'F'*&\"\")F'%&alphaGF'!\"\"F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "cond3d:=(1/6)*coeff(coeff(Y3,D[2](f)(x0,y0)),D[1](f) (x0,y0))=(1/2)*coeff(coeff(Fi20,D[2](f)(x0,y0)),D[1](f)(x0,y0));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3dG/#\"\"\"\"\"'\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "cond3e:=(1/6)*coeff(coeff(Y 3,D[2](f)(x0,y0)^2),f(x0,y0))=(1/2)*coeff(coeff(Fi20,D[2](f)(x0,y0)^2) ,f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3eG/#\"\"\"\"\"' \"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 264 2 "b)" }}}{EXCHG {PARA 0 " " 0 "" {TEXT 270 23 "funci\363n de estabilidad " }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface(labeling=false):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=(x,y)->lambda*y;" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%\"fGf*6$%\"xG%\"yG6\"6$%)operatorG%&arrowGF)*&%'lambdaG\"\"\"9%F/F )F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "k1_:=f(x0,y0);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k1_G*&%'lambdaG\"\"\"%#y0GF'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "k2_:=f(x0+1/(2*alpha)*h,y0+1 /(2*alpha)*h*k1_);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k2_G*&%'lambd aG\"\"\",&%#y0GF'*,\"\"#!\"\"%&alphaGF,%\"hGF'F&F'F)F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "y1:=expand(y0+h*((1-alpha)*k1_+alph a*k2_));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G,(%#y0G\"\"\"*(%\"hG F'%'lambdaGF'F&F'F'*&#F'\"\"#F'*()F*F-F')F)F-F'F&F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "y1:=collect(subs(lambda=z/h,y1),y0) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G*&,(\"\"\"F'%\"zGF'*&#F'\" \"#F'*$)F(F+F'F'F'F'%#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$%)operatorG%&arrowGF(,(\"\"\"F-9$F- *&#F-\"\"#F-*$)F.F1F-F-F-F(F(F(" }}}}{MARK "0 0 0" 10 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }