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"Maple Input Placeholder" -1 207 "Courier New" 1 12 200 0 200 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "E quation Label" -1 208 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 } {CSTYLE "Hyperlink" -1 17 "Times" 1 12 0 128 128 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "Caption Text" -1 209 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 144 "ynp1:=a0*y(tn)+a1*y(tn-h)+a2*y(tn- 2*h)+\n h*(bm1*D(y)(tn+h)+b0*D(y)(tn)+b1*D(y)(tn-h)+\n b2 *D(y)(tn-2*h))+E5*h^5*(D@@5)(y)(theta)/5!;" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%ynp1G6\",,*&I#a0GF$\"\"\"-I\"yGF$6#I#tnGF$F(F(*&I#a1GF $F(-F*6#,&F,F(I\"hGF$!\"\"F(F(*&I#a2GF$F(-F*6#,&F,F(F2!\"#F(F(*&F2F(,* *&I$bm1GF$F(--I\"DG6$%*protectedGI(_syslibGF$6#F*6#,&F,F(F2F(F(F(*&I#b 0GF$F(-F?F+F(F(*&I#b1GF$F(-F?F0F(F(*&I#b2GF$F(-F?F7F(F(F(F(*(I#E5GF$F( F2\"\"&---I#@@GFA6$F@FRFD6#I&thetaGF$F(#F(\"$?\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "r:=y(tn+h)-ynp1;" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I\"rG6\",.-I\"yGF$6#,&I#tnGF$\"\"\"I\"hGF$F+F+*&I#a0GF$F +-F'6#F*F+!\"\"*&I#a1GF$F+-F'6#,&F*F+F,F1F+F1*&I#a2GF$F+-F'6#,&F*F+F,! \"#F+F1*&F,F+,**&I$bm1GF$F+--I\"DG6$%*protectedGI(_syslibGF$6#F'F(F+F+ *&I#b0GF$F+-FBF0F+F+*&I#b1GF$F+-FBF5F+F+*&I#b2GF$F+-FBF:F+F+F+F1*(I#E5 GF$F+F,\"\"&---I#@@GFD6$FCFSFG6#I&thetaGF$F+#F1\"$?\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "eq[0]:=eval(subs(y=(x->1),r));" }} {PARA 11 "" 1 "" {XPPMATH 20 ">&I#eqG6\"6#\"\"!,*\"\"\"F)I#a0GF%!\"\"I #a1GF%F+I#a2GF%F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "for j from 1 to 5 do\n tmp[j]:=eval(subs(y=(x->x^j),r));\n eq[j]:=coe ff(tmp[j],h^j);\n print(eq[j]);\nod:" }}{PARA 11 "" 1 "" {XPPMATH 20 ",0\"\"\"F#I#a1G6\"F#I#a2GF%\"\"#I$bm1GF%!\"\"I#b0GF%F)I#b1GF%F)I#b 2GF%F)" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.\"\"\"F#I#a1G6\"!\"\"I#a2GF% !\"%I$bm1GF%!\"#I#b1GF%\"\"#I#b2GF%\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",.\"\"\"F#I#a1G6\"F#I#a2GF%\"\")I$bm1GF%!\"$I#b1GF%F)I#b2GF%!#7" } }{PARA 11 "" 1 "" {XPPMATH 20 ",.\"\"\"F#I#a1G6\"!\"\"I#a2GF%!#;I$bm1G F%!\"%I#b1GF%\"\"%I#b2GF%\"#K" }}{PARA 11 "" 1 "" {XPPMATH 20 ",0\"\" \"F#I#a1G6\"F#I#a2GF%\"#KI$bm1GF%!\"&I#b1GF%F)I#b2GF%!#!)I#E5GF%!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "S1:=solve(\{seq(eq[k],k= 0..5)\},\{a0,bm1,b0,b1,b2,E5\});" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#S 1G6\"<(/I#E5GF$,(#!#>\"\"'\"\"\"I#a1GF$#\"#6F+I#a2GF$#!\"%\"\"$/I#a0GF $,(F,F,F-!\"\"F0F7/I#b0GF$,(#\"#>\"#CF,F-#\"#8F=F0#F,F3/I#b1GF$,(#!\"& F=F,F-F>F0#\"\"%F3/I#b2GF$,(#F,F=F,F-#F7F=F0F@/I$bm1GF$,&#F3\"\")F,F-F L" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "method:=subs(E5=0,ynp1 );" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I'methodG6\",**&I#a0GF$\"\"\"-I\" yGF$6#I#tnGF$F(F(*&I#a1GF$F(-F*6#,&F,F(I\"hGF$!\"\"F(F(*&I#a2GF$F(-F*6 #,&F,F(F2!\"#F(F(*&F2F(,**&I$bm1GF$F(--I\"DG6$%*protectedGI(_syslibGF$ 6#F*6#,&F,F(F2F(F(F(*&I#b0GF$F(-F?F+F(F(*&I#b1GF$F(-F?F0F(F(*&I#b2GF$F (-F?F7F(F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "m2:=subs( S1,method);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#m2G6\",**&,(\"\"\"F(I# a1GF$!\"\"I#a2GF$F*F(-I\"yGF$6#I#tnGF$F(F(*&F)F(-F-6#,&F/F(I\"hGF$F*F( F(*&F+F(-F-6#,&F/F(F4!\"#F(F(*&F4F(,**&,&#\"\"$\"\")F(F)#F*\"#CF(--I\" DG6$%*protectedGI(_syslibGF$6#F-6#,&F/F(F4F(F(F(*&,(#\"#>FBF(F)#\"#8FB F+#F(F?F(-FDF.F(F(*&,(#!\"&FBF(F)FPF+#\"\"%F?F(-FDF2F(F(*&,(#F(FBF(F)F AF+FRF(-FDF7F(F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "m3: =eval(subs(D(y)=(x->f(x,y(x))),m2));" }}{PARA 11 "" 1 "" {XPPMATH 20 " >I#m3G6\",**&,(\"\"\"F(I#a1GF$!\"\"I#a2GF$F*F(-I\"yGF$6#I#tnGF$F(F(*&F )F(-F-6#,&F/F(I\"hGF$F*F(F(*&F+F(-F-6#,&F/F(F4!\"#F(F(*&F4F(,**(,&#\" \"$\"\")F(F)#F*\"#CF(I\"AGF$F(-F-6#,&F/F(F4F(F(F(*(,(#\"#>FBF(F)#\"#8F BF+#F(F?F(FCF(F,F(F(*(,(#!\"&FBF(F)FKF+#\"\"%F?F(FCF(F1F(F(*(,(#F(FBF( F)FAF+FMF(FCF(F6F(F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=(xi,eta)->A*eta;" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I\"fG6\"f*6$I#x iGF$I$etaGF$F$6$I)operatorGF$I&arrowGF$F$*&I\"AGF$\"\"\"9%F.F$F$F$" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "m4:=y(tn+h)=m3;" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I#m4G6\"/-I\"yGF$6#,&I#tnGF$\"\"\"I\"hGF$F+,**& ,(F+F+I#a1GF$!\"\"I#a2GF$F1F+-F'6#F*F+F+*&F0F+-F'6#,&F*F+F,F1F+F+*&F2F +-F'6#,&F*F+F,!\"#F+F+*&F,F+,**(,&#\"\"$\"\")F+F0#F1\"#CF+I\"AGF$F+F&F +F+*(,(#\"#>FFF+F0#\"#8FFF2#F+FCF+FGF+F3F+F+*(,(#!\"&FFF+F0FLF2#\"\"%F CF+FGF+F6F+F+*(,(#F+FFF+F0FEF2FNF+FGF+F:F+F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "ceq:=eval(subs(y=(s->rho^s),m4));" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I$ceqG6\"/)I$rhoGF$,&I#tnGF$\"\"\"I\"hGF$F*,**& ,(F*F*I#a1GF$!\"\"I#a2GF$F0F*)F'F)F*F**&F/F*)F',&F)F*F+F0F*F**&F1F*)F' ,&F)F*F+!\"#F*F**&F+F*,**(,&#\"\"$\"\")F*F/#F0\"#CF*I\"AGF$F*F&F*F**(, (#\"#>FBF*F/#\"#8FBF1#F*F?F*FCF*F2F*F**(,(#!\"&FBF*F/FHF1#\"\"%F?F*FCF *F4F*F**(,(#F*FBF*F/FAF1FJF*FCF*F7F*F*F*F*" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 37 "ceq2:=subs(\{a1=1,a2=1,tn=1,h=1\},ceq);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%ceq2G6\"/*$I$rhoGF$\"\"#,0F'!\"\"\"\"\"F+*$F' F*F+*&I\"AGF$F+F'F(#F+\"\"$*&F.F+F'F+#\"\"&F0F.F2*&F.F+F'F*F/" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "S2:=solve(ceq2,rho);" }} {PARA 11 "" 1 "" {XPPMATH 20 ">I#S2G6\"6%!\"\",$*&,&I\"AGF$\"\"#*$,&*$ F*F+\"\"$\"\"*\"\"\"#F1F+F&F1,&F*F1!\"$F1F&F&,$*&,&F*F+F,F1F1F3F&F&" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 125 100 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }