{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 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 1 18 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 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 265 "" 1 18 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 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 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 "Ti mes" 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 } {PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 263 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 264 48 "(3) Ecuaciones escalares: m\351todos de RUNGE- KUTTA" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 262 15 "Ejercicio 03-14" }}{PARA 4 "" 0 "" {TEXT -1 88 "\nConsid\351rese la f amilia de m\351todos de Runge-Kutta de 3 etapas y expl\355citos para l os que," }}{PARA 4 "" 0 "" {TEXT -1 9 "adem\341s, " }{XPPEDIT 18 0 "c [2];" "6#&%\"cG6#\"\"#" }{TEXT -1 3 " = " }{XPPEDIT 18 0 "c[3];" "6#&% \"cG6#\"\"$" }{TEXT -1 7 " y " }{XPPEDIT 18 0 "b[2];" "6#&%\"bG6# \"\"#" }{TEXT -1 3 " = " }{XPPEDIT 18 0 "b[3];" "6#&%\"bG6#\"\"$" } {TEXT -1 7 " y " }{XPPEDIT 18 0 "a[3,1];" "6#&%\"aG6$\"\"$\"\"\"" }{TEXT -1 57 " = 0 . De entre ellos se buscaran los que proporcionen e l" }}{PARA 4 "" 0 "" {TEXT -1 15 "orden mas alto." }}}{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 32 " c[3]:=c[2]:b[3]:=b[2]:a[3,1]:=0:" }}}{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:=diff(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):" }}} {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):" }}} {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 259 2 "a)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 27 "condiciones para el orden 1" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 44 "Fi_0:=expand(b[1]*k1_0+b[2]*k2_0+b[3]*k3_0);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi_0G,&*&&%\"bG6#\"\"\"F*-%\"fG6$%# x0G%#y0GF*F**(\"\"#F*&F(6#F1F*F+F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "cond1a:=coeff(Y1,f(x0,y0))=coeff(Fi_0,f(x0,y0));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond1aG/\"\"\",&&%\"bG6#F&F&*&\"\"# F&&F)6#F,F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 27 "condiciones par a el orden 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "Fi10:=expan d(b[1]*k110+b[2]*k210+b[3]*k310);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %%Fi10G,(**\"\"#\"\"\"&%\"bG6#F'F(--&%\"DG6#F(6#%\"fG6$%#x0G%#y0GF(&% \"cGF+F(F(**F)F(--&F/F+F1F3F(&%\"aG6$F'F(F(-F2F3F(F(**F)F(F9F(&F=6$\" \"$F'F(F?F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "cond2a:=(1 /2)*coeff(Y2,D[1](f)(x0,y0))=coeff(Fi10,D[1](f)(x0,y0));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%'cond2aG/#\"\"\"\"\"#,$*(F(F'&%\"bG6#F(F'&%\"c GF-F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "cond2b:=(1/2)*co eff(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$F(F'F'F'*&F+F'&F/6$\"\"$F(F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "sol1:=solve(\{cond1a,cond2a,cond2b \});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%sol1G<'/&%\"aG6$\"\"$\"\"#, $*&#\"\"\"F+F/*&,&F/!\"\"*(F+F/&%\"bG6#F+F/&F(6$F+F/F/F/F/F4F2F/F2/&F5 6#F/,&F/F/*&F+F/F4F/F2/&%\"cGF6,$*&#F/\"\"%F/*&F/F/F4F2F/F//F4F4/F7F7 " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 2 "b)" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 258 28 "condiciones para el orden 3 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "Fi20:=expand(b[1]*k120+b[2]*k220+b[3]*k320);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%%Fi20G,0**\"\"#\"\"\"&%\"bG6#F'F(--& %\"DG6$F(F(6#%\"fG6$%#x0G%#y0GF()&%\"cGF+F'F(F(*.F'F(F)F(F7F(--&F/6$F( F'F1F3F(&%\"aG6$F'F(F(-F2F3F(F(**F)F()F>F'F()FAF'F(--&F/6$F'F'F1F3F(F( *.F'F(F)F(F7F(F:F(&F?6$\"\"$F'F(FAF(F(**F)F()FJF'F(FDF(FEF(F(*.F'F(F)F (--&F/F+F1F3F(FJF(--&F/6#F(F1F3F(F7F(F(*.F'F(F)F()FPF'F(FJF(F>F(FAF(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/#\"\"\"\"\"'*&&%\"bG6#\"\"#F')&%\"cGF,F -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(coeff(Fi20,D[1,2](f) (x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3bG/#\" \"\"\"\"$,&*(&%\"bG6#\"\"#F'&%\"cGF-F'&%\"aG6$F.F'F'F'*(F+F'F/F'&F26$F (F.F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "cond3c:=(1/6)*c oeff(coeff(Y3,D[2,2](f)(x0,y0)),f(x0,y0)^2)=(1/2)*coeff(coeff(Fi20,D[2 ,2](f)(x0,y0)),f(x0,y0)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond 3cG/#\"\"\"\"\"',&*&#F'\"\"#F'*&&%\"bG6#F,F')&%\"aG6$F,F'F,F'F'F'*&F+F '*&F.F')&F36$\"\"$F,F,F'F'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/#\"\"\"\"\"'*(&%\"bG6#\"\"#F'&%\"cGF,F' &%\"aG6$\"\"$F-F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "cond3 e:=(1/6)*coeff(coeff(Y3,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/#\"\"\"\"\"'*(&%\"bG6#\"\"#F'&%\"aG6$\"\"$F-F'&F/6$F-F'F'" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "sol2:=solve(\{cond1a,cond2 a,cond2b,cond3a,cond3b,cond3c,cond3d,cond3e\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%sol2G<'/&%\"cG6#\"\"##F*\"\"$/&%\"bGF)#F,\"\")/&F/6# \"\"\"#F5\"\"%/&%\"aG6$F*F5F+/&F:6$F,F*F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 261 6 "metodo" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 " " {TEXT 266 12 " 0 | " }}{PARA 4 "" 0 "" {TEXT 267 18 " 2/3 \+ | 2/3" }}{PARA 4 "" 0 "" {TEXT 270 27 " 2/3 | 0 2/ 3" }}{PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 268 21 "------- --------------" }}{PARA 4 "" 0 "" {TEXT 269 36 " | 1/4 \+ 3/8 3/8" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 265 45 "que suele llamarse de NYSTR\326M de tercer orden" }}}} {MARK "0 3 0" 15 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }