{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 1 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "Lax-Wendroffovo schema - m odifikavana rovnice vcetne 4. derivace u_xxxx" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "d1:= (u(n+1,i) - u(n,i))/dt + a*(u(n,i+1) - u(n,i-1))/(2*dx) - \+ a^2*dt/(2*dx^2)*(u(n,i+1) - 2*u(n,i) + u(n,i-1));\n" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%#d1G,(*&,&-%\"uG6$,&%\"nG\"\"\"F-F-%\"iGF--F)6$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 "Order:=5;\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&OrderG\"\"&" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 122 "u := (argn,argi) -> \n convert(mtaylor(\n \+ uu(t + dt*(argn - n),x+dx*(argi - i)),\n [dt=0,dx=0],Order), polynom);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uGf*6$%%argnG%%argi G6\"6$%)operatorG%&arrowGF)-%(convertG6$-%(mtaylorG6%-%#uuG6$,&%\"tG\" \"\"*&%#dtGF8,&9$F8%\"nG!\"\"F8F8,&%\"xGF8*&%#dxGF8,&9%F8%\"iGF>F8F87$ /F:\"\"!/FBFH%&OrderG%(polynomGF)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "eq1 := simplify(d1);dt := lambda*dx;\n" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#>%$eq1G,2*&#\"\"\"\"#CF(*&--&%\"DG6&F(F(F(F(6#%# uuG6$%\"tG%\"xGF()%#dtG\"\"$F(F(F(*&#F(\"\"'F(*&--&F.6%F(F(F(F0F2F()F6 \"\"#F(F(F(*&#F(FAF(*&--&F.6$F(F(F0F2F(F6F(F(F(--&F.6#F(F0F2F(*&F9F(*( --&F.6%FAFAFAF0F2F(%\"aGF()%#dxGFAF(F(F(*&--&F.6#FAF0F2F(FSF(F(*&#F(F) F(**--&F.6&FAFAFAFAF0F2F()FSFAF(F6F(FTF(F(!\"\"*&#F(FAF(*(--&F.6$FAFAF 0F2F(F\\oF(F6F(F(F]o" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dtG*&%'lamb daG\"\"\"%#dxGF'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 73 "dosazeni za c asove derivace primo z advekcni rovnice dava spatny vysledek" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 155 "collect(subs(D[1$2](uu)(t,x ) = a^2*D[2$2](uu)(t,x),\n D[1$3](uu)(t,x) = -a^3*D[2$3](uu)(t,x), \n D[1$4](uu)(t,x) = a^4*D[2$4](uu)(t,x),eq1),D,factor);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,*--&%\"DG6#\"\"\"6#%#uuG6$%\"tG%\"xGF)*&--& F'6#\"\"#F*F,F)%\"aGF)F)*&#F)\"\"'F)*,F5F))%#dxGF4F),&*&F5F)%'lambdaGF )F)F)!\"\"F),&*&F5F)F>F)F)F)F)F)--&F'6%F4F4F4F*F,F)F)F?*&#F)\"#CF)*.)F 5F4F)F>F))F;\"\"$F)F " 0 "" {MPLTEXT 1 0 33 " sol := solve(eq1,D[1](uu)(t,x));\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6# >%$solG,0*&#\"\"\"\"#CF(*(--&%\"DG6&F(F(F(F(6#%#uuG6$%\"tG%\"xGF()%'la mbdaG\"\"$F()%#dxGF7F(F(!\"\"*&#F(\"\"'F(*(--&F.6%F(F(F(F0F2F()F6\"\"# F()F9FDF(F(F:*&#F(FDF(*(--&F.6$F(F(F0F2F(F6F(F9F(F(F:*&#F(F=F(*(--&F.6 %FDFDFDF0F2F(%\"aGF(FEF(F(F:*&--&F.6#FDF0F2F(FTF(F:*&#F(F)F(**--&F.6&F DFDFDFDF0F2F()FTFDF(F6F(F8F(F(F(*&#F(FDF(**--&F.6$FDFDF0F2F(F[oF(F6F(F 9F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "eq2 := collect(a lgsubs(dx^4=0,simplify(subs(D[1$2](uu)(t,x) = diff(sol,t$1),eq1))),dx) ;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$eq2G,,*&,(*&#\"\"\"\"#CF**&--& %\"DG6&F*F*F*F*6#%#uuG6$%\"tG%\"xGF*)%'lambdaG\"\"$F*F*!\"\"*&#F*\"#7F **(F8F*--&F06&F*\"\"#FCFCF2F4F*%\"aGF*F*F:*&#F*F+F**(--&F06&FCFCFCFCF2 F4F*)FDFCF*F8F*F*F:F*)%#dxGF9F*F**&,&*&#F*FCF**(F8F*--&F06$F*FCF2F4F*F DF*F*F:*&#F*FCF**(--&F06$FCFCF2F4F*FLF*F8F*F*F:F*FNF*F**&,(*&#F*F=F**& --&F06%F*F*F*F2F4F*)F8FCF*F*F:*&#F*\"\"%F**(FboF*--&F06%F*FCFCF2F4F*FL F*F*F**&#F*\"\"'F**&--&F06%FCFCFCF2F4F*FDF*F*F*F*)FNFCF*F**&--&F06#FCF 2F4F*FDF*F*--&F06#F*F2F4F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "eq3 := collect(algsubs(dx^4=0,simplify(subs(D[1,2](uu)(t,x) = diff (sol,x),eq2))),dx);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$eq3G,**&,**& #\"\"\"\"#CF**&--&%\"DG6&F*F*F*F*6#%#uuG6$%\"tG%\"xGF*)%'lambdaG\"\"$F *F*!\"\"*&#F*\"#7F**(F8F*--&F06&F*\"\"#FCFCF2F4F*%\"aGF*F*F:*&#F*F+F** (--&F06&FCFCFCFCF2F4F*)FDFCF*F8F*F*F**&#F*F=F**(FDF*F7F*--&F06&F*F*F*F CF2F4F*F*F*F*)%#dxGF9F*F**&,,*&#F*\"\"%F**(FDF*)F8FCF*--&F06%F*F*FCF2F 4F*F*F**&#F*FZF**()FDF9F*--&F06%FCFCFCF2F4F*FfnF*F*F:*&#F*F=F**&--&F06 %F*F*F*F2F4F*FfnF*F*F:*&FYF**(FfnF*--&F06%F*FCFCF2F4F*FLF*F*F**&#F*\" \"'F**&F_oF*FDF*F*F*F*)FUFCF*F**&--&F06#FCF2F4F*FDF*F*--&F06#F*F2F4F* " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "eq4 := collect(algsubs( dx^4=0,simplify(subs(D[1$3](uu)(t,x) = diff(sol,t$2),eq3))),dx);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%$eq4G,**&,**&#\"\"\"\"#7F**(%'lambda GF*--&%\"DG6&F*\"\"#F3F36#%#uuG6$%\"tG%\"xGF*%\"aGF*F*!\"\"*&#F*\"#CF* *(--&F16&F3F3F3F3F4F6F*)F9F3F*F-F*F*F**&#F*F+F**(F9F*)F-\"\"$F*--&F16& F*F*F*F3F4F6F*F*F**&#F*F=F**(FGF*--&F16&F*F*F3F3F4F6F*FCF*F*F:F*)%#dxG FHF*F**&,**&#F*FHF**(F9F*)F-F3F*--&F16%F*F*F3F4F6F*F*F**&#F*\"\"%F**() F9FHF*--&F16%F3F3F3F4F6F*FenF*F*F:*&#F*F\\oF**(FenF*--&F16%F*F3F3F4F6F *FCF*F*F**&#F*\"\"'F**&F_oF*F9F*F*F*F*)FUF3F*F**&--&F16#F3F4F6F*F9F*F* --&F16#F*F4F6F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "eq5 := c ollect(algsubs(dx^4=0,simplify(subs(D[1$2,2](uu)(t,x) = diff(sol,t,x), eq4))),dx);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$eq5G,**&,,*&#\"\"\" \"#7F**(%'lambdaGF*--&%\"DG6&F*\"\"#F3F36#%#uuG6$%\"tG%\"xGF*%\"aGF*F* !\"\"*&#F*\"#CF**(--&F16&F3F3F3F3F4F6F*)F9F3F*F-F*F*F**&#F*F+F**(F9F*) F-\"\"$F*--&F16&F*F*F*F3F4F6F*F*F:*&#F*F=F**(FGF*--&F16&F*F*F3F3F4F6F* FCF*F*F:*&#F*\"\"'F**()F9FHF*FGF*F.F*F*F*F*)%#dxGFHF*F**&,(*&#F*F+F**( )F-F3F*--&F16%F*F3F3F4F6F*FCF*F*F:*&#F*\"\"%F**(FXF*--&F16%F3F3F3F4F6F *FjnF*F*F:*&FUF**&FcoF*F9F*F*F*F*)FZF3F*F**&--&F16#F3F4F6F*F9F*F*--&F1 6#F*F4F6F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "eq6 := collec t(algsubs(dx^4=0,simplify(subs(D[1,2$2](uu)(t,x) = diff(sol,x$2),eq5)) ),dx);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$eq6G,**&,,*&#\"\"\"\"#7F* *(%'lambdaGF*--&%\"DG6&F*\"\"#F3F36#%#uuG6$%\"tG%\"xGF*%\"aGF*F*!\"\"* &#F*\"#CF**(--&F16&F3F3F3F3F4F6F*)F9F3F*F-F*F*F**&#F*F+F**(F9F*)F-\"\" $F*--&F16&F*F*F*F3F4F6F*F*F:*&#F*\"\"'F**()F9FHF*FGF*F.F*F*F**&#F*F=F* *()F9\"\"%F*F?F*FGF*F*F:F*)%#dxGFHF*F**&,&*&#F*FOF**(FQF*--&F16%F3F3F3 F4F6F*)F-F3F*F*F:*&FNF**&FhnF*F9F*F*F*F*)FXF3F*F**&--&F16#F3F4F6F*F9F* F*--&F16#F*F4F6F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "eq7 := collect(algsubs(dx^4=0,expand(subs(D[1$3,2](uu)(t,x) = diff(sol,t$2,x ),eq6))),dx);\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$eq7G,**&,,*&#\" \"\"\"#7F**()%'lambdaG\"\"$F*--&%\"DG6&F*F*\"\"#F56#%#uuG6$%\"tG%\"xGF *)%\"aGF5F*F*F**&#F*F+F**(F.F*--&F36&F*F5F5F5F6F8F*F " 0 "" {MPLTEXT 1 0 94 "eq8 := collect(algsubs(dx^4=0,simplify(subs(D[1$2,2$2](uu)(t,x) = \+ diff(sol,t,x$2),eq7))),dx);\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$eq 8G,**&,**&#\"\"\"\"#7F**()%\"aG\"\"$F*)%'lambdaGF/F*--&%\"DG6&F*\"\"#F 7F76#%#uuG6$%\"tG%\"xGF*F*F**&#F*F+F**(F1F*F2F*F.F*F*!\"\"*&#F*\"#CF** (--&F56&F7F7F7F7F8F:F*)F.F7F*F1F*F*F**&#F*FCF**()F.\"\"%F*FEF*F0F*F*F@ F*)%#dxGF/F*F**&,&*&#F*\"\"'F**(F-F*--&F56%F7F7F7F8F:F*)F1F7F*F*F@*&#F *FUF**&FWF*F.F*F*F*F*)FPF7F*F**&--&F56#F7F8F:F*F.F*F*--&F56#F*F8F:F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "eq9 := collect(algsubs(dx ^4=0,simplify(subs(D[1,2$3](uu)(t,x) = diff(sol,x$3),eq8))),D,factor); \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq9G,*--&%\"DG6#\"\"\"6#%#uuG 6$%\"tG%\"xGF+*&--&F)6#\"\"#F,F.F+%\"aGF+F+*&#F+\"\"'F+*,F7F+)%#dxGF6F +,&*&F7F+%'lambdaGF+F+F+!\"\"F+,&*&F7F+F@F+F+F+F+F+--&F)6%F6F6F6F,F.F+ F+FA*&#F+\"\")F+*.)F7F6F+F@F+)F=\"\"$F+F>F+FBF+--&F)6&F6F6F6F6F,F.F+F+ FA" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "18 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }