{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 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 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 47 "norm2 := (arg) -> simplify(arg*subs (I=-I,arg));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&norm2Gf*6#%$argG6\" 6$%)operatorG%&arrowGF(-%)simplifyG6#*&9$\"\"\"-%%subsG6$/^#F1^#!\"\"F 0F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "d1:= (u(n+1,j) - u(n-1,j))/(2*dt) + a*(u(n,j+1)- u(n,j-1))/(2*dx);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#d1G,&*&#\"\"\"\"\"#F(*&,&-%\"uG6$,&%\"nGF(F(F(% \"jGF(-F-6$,&F0F(F(!\"\"F1F5F(%#dtGF5F(F(*&F'F(*(%\"aGF(,&-F-6$F0,&F1F (F(F(F(-F-6$F0,&F1F(F(F5F5F(%#dxGF5F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "u := (argn,argj) -> g^(argn - n)*\n \+ convert(exp(I*(argj - j)*Theta),trig);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uGf*6$%%argnG%%argjG6\"6$%)operatorG%&arrowGF)*&)% \"gG,&9$\"\"\"%\"nG!\"\"F2-%(convertG6$-%$expG6#*(,&9%F2%\"jGF4F2%&The taGF2^#F2F2%%trigGF2F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "d1;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(\"\"#!\"\",&%\"gG\"\" \"*&F)F)F(F&F&F)%#dtGF&F)**%\"aGF)-%$sinG6#%&ThetaGF)%#dxGF&^#F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "gsol := solve(d1,g);\n" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%gsolG6$*(^#!\"\"\"\"\",&*(-%$sinG6 #%&ThetaGF)%\"aGF)%#dtGF)F)*$,&*()F,\"\"#F))F0F6F))F1F6F)F)*$)%#dxGF6F )F(#F)F6F)F)F;F(*(,&F+F(F2F)F)F;F(^#F)F)" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "g1 := algsu bs(cos(Theta)^2=1-sin(Theta)^2,simplify(subs(dt=lambda*dx,gsol[1]))); \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#g1G*(^#!\"\"\"\"\"%#dxGF',&** -%$sinG6#%&ThetaGF(%\"aGF(%'lambdaGF(F)F(F(*$,$*&)F)\"\"#F(,&*()F,F6F( )F0F6F()F1F6F(F'F(F(F(F'#F(F6F(F(" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "g2 := simplify(no rm2(g1));\nassume(dx>0);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#g2G*$ ),&*(-%$sinG6#%&ThetaG\"\"\"%\"aGF-%'lambdaGF-F-*$,(*()F.\"\"#F-)-%$co sGF+F4F-)F/F4F-!\"\"*&F3F-F8F-F-F-F9#F-F4F-F4F-" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}}{MARK "10 0 0" 0 }{VIEWOPTS 1 1 0 2 1 1805 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }