{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 } {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 32 "unassign('u');readli b(mtaylor);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6\"6*%\"fG%\"kG%\"v G%\"mG%\"nG%\"sG%\"tG%\"wG6#%aoCopyright~(c)~1991~by~the~University~of ~Waterloo.~All~rights~reserved.GF$C2>8$&9\"6#\"\"\">8&&F46#\"\"#@&-%%t ypeG6$F8%$setG>F87#-%#opG6#F84-F>6$F8%%listG>F87#F8@$4-F>6$F8-FI6#<$%% nameG/FS%*algebraicGYQGinvalid~2nd~argument~(expansion~point)F$>8)-%$m apG6$f*6#%\"xGF$F$F$@%-F>6$9$%\"=G-%$rhsG6#F]o\"\"!F$F$F$F8>F8-Fen6$f* FhnF$F$F$@%F[o-%$lhsGFaoF]oF$F$F$F8>8'-%%nopsGFE@$0F[p-F]p6#<#FCYQHvar iables~(2nd~argument)~must~be~uniqueF$@%/9#F;>8(%&OrderG>Fip&F46#\"\"$ @%/Fgp\"\"%>8+&F46#Faq>Fcq7#-%\"$G6$F6F[p@$4-F>6$F8<$-F@6#FS-FIFarYQQ2 nd~argument~(the~variable(s))~must~be~a~name(s)F$@$34-F>6$Fip%*nonnegi ntG0Fip%)infinityGYQX3rd~argument~(the~order)~must~be~a~non-negative~i ntegerF$@$54-F>6$Fcq-FI6#%'posintG0-F]p6#FcqF[pYQen4th~argument~(weigh ts)~must~be~a~list~of~positive~integersF$>F2-%%subsG6$7#-%$seqG6$/&F86 #8%,&*&FetF6)8*&FcqFftF6F6&FYFftF6/Fgt;F6F[pF2>F2-Fen6&%(collectG-F^t6 $/-%\"OGF5Fbo-%'taylorG6%F2F[uFipF8.%,distributedG>F2-F^t6$7#-Fbt6$/Fe t,&FetF6F]u!\"\"F^u-F^t6$/F[uF6F2F$F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "d1:= (u(n+1,j) - u(n,j))/dt + a*(u(n,j+1) - u(n,j-1) )/(2*dx) \n - a^2*dt/(2*dx^2)*(u(n,j+1) - 2*u(n,j) + u(n,j-1));\n " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#d1G,(*&,&-%\"uG6$,&%\"nG\"\"\"F -F-%\"jGF--F)6$F,F.!\"\"F-%#dtGF1F-*&#F-\"\"#F-*(%\"aGF-,&-F)6$F,,&F.F -F-F-F--F)6$F,,&F.F-F-F1F1F-%#dxGF1F-F-*&#F-F5F-**F7F5F2F-F?!\"#,(F9F- *&F5F-F/F-F1F " 0 "" {MPLTEXT 1 0 10 "O rder:=4;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&OrderG\"\"%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 124 "u := (argn,argj) -> \n c onvert(mtaylor(\n uu(t + dt*(argn - n),x+dx*(argj - j)),\n [ dt=0,dx=0],Order),polynom); \n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>% \"uGf*6$%%argnG%%argjG6\"6$%)operatorG%&arrowGF)-%(convertG6$-%(mtaylo rG6%-%#uuG6$,&%\"tG\"\"\"*&%#dtGF8,&9$F8%\"nG!\"\"F8F8,&%\"xGF8*&%#dxG F8,&9%F8%\"jGF>F8F87$/F:\"\"!/FBFH%&OrderG%(polynomGF)F)F)" }}}{PARA 11 "" 1 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "u (n+1,j+1);\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,6-%#uuG6$%\"tG%\"xG\" \"\"*&--&%\"DG6#F)6#F%F&F)%#dtGF)F)*&--&F.6#\"\"#F0F&F)%#dxGF)F)*&#F)F 7F)*&--&F.6$F)F)F0F&F))F1F7F)F)F)*(F1F)--&F.6$F)F7F0F&F)F8F)F)*&F:F)*& --&F.6$F7F7F0F&F))F8F7F)F)F)*&#F)\"\"'F)*&)F1\"\"$F)--&F.6%F)F)F)F0F&F )F)F)*&F:F)*(F@F)--&F.6%F)F)F7F0F&F)F8F)F)F)*&F:F)*(F1F)FLF)--&F.6%F)F 7F7F0F&F)F)F)*&FNF)*&)F8FRF)--&F.6%F7F7F7F0F&F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "simplify(d1);\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,.--&%\"DG6#\"\"\"6#%#uuG6$%\"tG%\"xGF)*&#F)\"\"#F)*&-- &F'6$F)F)F*F,F)%#dtGF)F)F)*&#F)\"\"'F)*&)F7F1F)--&F'6%F)F)F)F*F,F)F)F) *&%\"aGF)--&F'6#F1F*F,F)F)*&F9F)*(FBF))%#dxGF1F)--&F'6%F1F1F1F*F,F)F)F )*&#F)F1F)*()FBF1F)F7F)--&F'6$F1F1F*F,F)F)!\"\"" }}}{EXCHG {PARA 11 " " 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "unas sign('u');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "u(i);\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{MARK "9 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }