{VERSION 6 0 "IBM INTEL LINUX" "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 0 0 0 0 0 0 2 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 "big" -1 256 "courier" 1 24 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "norm2 := (arg) -> simplify(arg*subs (I=-I,arg));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&norm2Gf*6#%$argG6 \"6$%)operatorG%&arrowGF(-%)simplifyG6#*&9$\"\"\"-%%subsG6$/^#F1^#!\" \"F0F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "d1:= (u(n+1 ,j) - u(n,j))/dt + a*(u(n,j)- u(n,j-1))/dx;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#d1G,&*&,&-%\"uG6$,&%\"nG\"\"\"F-F-%\"jGF--F)6$F,F.! \"\"F-%#dtGF1F-*(%\"aGF-,&F/F--F)6$F,,&F.F-F-F1F1F-%#dxGF1F-" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "u := (argn,argj) -> g^(argn \+ - n)*\n convert(exp(I*(argj - j)*Theta),trig);\n " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uGf*6$%%argnG%%argjG6\"6$%)ope ratorG%&arrowGF)*&)%\"gG,&9$\"\"\"%\"nG!\"\"F2-%(convertG6$-%$expG6#*( ,&9%F2%\"jGF4F2%&ThetaGF2^#F2F2%%trigGF2F)F)F)" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 4 "d1;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&,& %\"gG\"\"\"F'!\"\"F'%#dtGF(F'*(%\"aGF',(F'F'-%$cosG6#%&ThetaGF(*&-%$si nGF/F'^#F'F'F'F'%#dxGF(F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "gsol := solve(d1,g);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%gsolG ,$*&,*%#dxG!\"\"*&%\"aG\"\"\"%#dtGF,F,*(F+F,F-F,-%$cosG6#%&ThetaGF,F)* *F+F,F-F,-%$sinGF1F,^#F,F,F,F,F(F)F)" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "g1 := simpl ify(subs(dt=lambda*dx,gsol));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%# g1G,*\"\"\"F&*&%\"aGF&%'lambdaGF&!\"\"*(F(F&F)F&-%$cosG6#%&ThetaGF&F&* *^#F*F&F(F&F)F&-%$sinGF.F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "g2 := simplify(norm2(g1));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%#g2G,,\"\"\"F&**\"\"#F&%\"aGF&%'lambdaGF&-%$cosG6#%&ThetaGF&F&**F(F& )F)F(F&)F*F(F&F+F&!\"\"*(F(F&F)F&F*F&F2*(F(F&F0F&F1F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "factor(g2-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*,\"\"#\"\"\"%\"aGF&%'lambdaGF&,&F&!\"\"*&F'F&F(F&F&F &,&-%$cosG6#%&ThetaGF&F&F*F&F*" }}}{PARA 11 "" 1 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "11 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }