{VERSION 6 0 "IBM INTEL NT" "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 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Text Output" -1 6 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 2 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}} {EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "ode := \{diff(u(x),x ,x)-u(x)+u(x)^2*(1+a(x)*x^2),\nD(u)(0)=0, D(u)(L)=0, diff(a(x),x), u(0 )=u0\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$odeG<'/--%\"DG6#%\"uG6# 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}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ppGf*6#%&x_ bvpG6(%$resG%%dataG%)solnprocG%&ndsolG%)outpointG%\"iG6#%inCopyright~( c)~2000~by~Waterloo~Maple~Inc.~All~rights~reserved.G6\"C)>%8_EnvDSNume ricSaveDigitsG%'DigitsG>F5\"#9@%/%-_EnvInFsolveG%%trueG>8(-&%&evalfG6# F46#9$>F=-F@FB>8%-%%evalG6#&%8&- _FG%$GetG6#Q/soln_procedureF1@$4-%%typeG6$F=.%(numericG@+/F=Q.solnproc edureF1O-FI6#FP-%'memberG6$F=7)Q&startF1Q%leftF1Q&rightF1Q*errorprocF1 Q(rawdataF1Q&orderF1Q&errorF1O-FPFB/F=Q(sysvarsF1O-FR6#F[p09!%(unknown GO-.F`pFBC$>8'-%(pointtoG6#&-FR6#Q0soln_proceduresF16#\"\"!O-.FgpFBZ%C $>8$-FP6#F=7$/%\"xG&FgqFM-%$seqG6$/&.7%-%\"aG6#F\\r-%\"uGFgr-%%diffG6$ FhrF\\r6#8)&Fgq6#,&F^sFNFNFN/F^s;FN\"\"$F1YF1F1F1F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "odeplot(pp, [[x, u(x)]], 0..L);" }}{PARA 13 "" 1 "" {GLPLOT2D 290 290 290 {PLOTDATA 2 "6$-%'CURVESG6$X,%)anythi ngG6\"6\"[gl'!%\"!!#_q\"S\"#00000000000000003FF7FFFFFFFFFFFE3FEA1F58D0 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{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "LL := NULL:\n" }}} {EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 249 "\nlprint(`[ a, u(0)]`);\nto 80 do\napprox := dsolve2approx(pp, 300):\npp := dsolve (ode, numeric, approxsoln=approx, continuation=la, maxmesh=3500, abser r=1e-4);\noo := (eval([a(x), u(x)], pp(0)));\nlprint(oo);\nLL := LL, [ op(oo), pp(0)]:\nu0 := u0*0.93:\nend:" }}{PARA 6 "" 1 "" {TEXT -1 11 " `[a, u(0)]`" }}{PARA 6 "" 1 "" {TEXT -1 46 "[-.352234615022477327e-6, \+ 1.49999999999999956]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.407924548027889 800e-1, 1.39499999999999934]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.6615505 20240090645e-1, 1.29734999999999934]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[ .768772649987101710e-1, 1.20653549999999976]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.745723940878636194e-1, 1.12207801500000004]" }}{PARA 6 "" 1 " " {TEXT -1 45 "[.630307768908460464e-1, 1.04353255399999956]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.488513771674385714e-1, .970485275199999275]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.372505820323222464e-1, .9025513058999 99989]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.289580168311799994e-1, .83937 2714500000060]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.230159251032216981e-1 , .780616624500000245]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.1861021896845 68056e-1, .725973460799999914]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.15237 4228790774502e-1, .675155318499999880]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.125908829889739386e-1, .627894446200000344]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.104758138444523922e-1, .583941835000000076]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.876175103675041860e-2, .543065906599999981]" }} {PARA 6 "" 1 "" {TEXT -1 45 "[.735813230052147216e-2, .505051293099999 854]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.619936351367744982e-2, .4696977 02600000212]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.523661335001641103e-2, \+ .436818863399999868]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.443265257763140 845e-2, .406241542999999984]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.3758542 57171567190e-2, .377804634999999778]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[ .319143070721965382e-2, .351358310599999890]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.271303477437434548e-2, .326763228899999814]" }}{PARA 6 "" 1 " " {TEXT -1 45 "[.230857149576374574e-2, .303889802899999894]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.196598022531593648e-2, .282617516699999904]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.167534842291982580e-2, .2628342905000 00067]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.142847842542416417e-2, .24443 5890200000061]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.121855541349076514e-2 , .227325377899999902]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.1039889271958 95038e-2, .211412601400000066]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.88771 1368970826778e-3, .196613719300000046]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.758012809513907912e-3, .182850758899999966]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.647414470984903658e-3, .170051205799999966]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.553061666494100236e-3, .158147621399999910]" }} {PARA 6 "" 1 "" {TEXT -1 45 "[.472538174467175565e-3, .147077287900000 020]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.403795596321339888e-3, .1367818 77699999998]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.345094997858083218e-3, \+ .127207146299999962]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.294958449206568 486e-3, .118302646100000032]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[.2521286 33820975043e-3, .110021460899999965]" }}{PARA 6 "" 1 "" {TEXT -1 45 "[ .215535032304677342e-3, .102319958599999969]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.184265545053859684e-3, .951575614999999736e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.157542594578389796e-3, .884965321999999916e-1]" }} {PARA 6 "" 1 "" {TEXT -1 48 "[.134702969199951658e-3, .823017749499999 757e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.115180765933316438e-3, .7654 06506999999904e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.98492954084297777 2e-4, .711828051499999865e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.842271 213160269180e-4, .662000087899999868e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.720310722844603882e-4, .615660081700000056e-1]" }}{PARA 6 "" 1 " " {TEXT -1 48 "[.616039725414700588e-4, .572563875999999792e-1]" }} {PARA 6 "" 1 "" {TEXT -1 48 "[.526888215394342202e-4, .532484404699999 914e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.450660351003458122e-4, .4952 10496399999880e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.38547982611655205 2e-4, .460545761699999792e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.329743 168080802778e-4, .428307558399999774e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.282079990920045855e-4, .398326029300000024e-1]" }}{PARA 6 "" 1 " " {TEXT -1 48 "[.241319074212639938e-4, .370443207199999958e-1]" }} {PARA 6 "" 1 "" {TEXT -1 48 "[.206459310587487446e-4, .344512182700000 142e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.176644982743071760e-4, .3203 96329899999902e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.15114464878983515 1e-4, .297968586800000068e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.129333 022574850910e-4, .277110785699999848e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.110675579164771768e-4, .257713030699999944e-1]" }}{PARA 6 "" 1 " " {TEXT -1 48 "[.947153497427327814e-5, .239673118600000068e-1]" }} {PARA 6 "" 1 "" {TEXT -1 48 "[.810616923905470595e-5, .222896000300000 022e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.693806053409755607e-5, .2072 93280300000252e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.59386527037090238 1e-5, .192782750700000068e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.508353 265510993566e-5, .179287958199999888e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.435182426502862954e-5, .166737801099999910e-1]" }}{PARA 6 "" 1 " " {TEXT -1 48 "[.372567708491741128e-5, .155066154999999994e-1]" }} {PARA 6 "" 1 "" {TEXT -1 48 "[.318982939244393022e-5, .144211524200000 066e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.273122845229869482e-5, .1341 16717499999962e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.23387119598566624 6e-5, .124728547299999966e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.200273 552229202711e-5, .115997548999999986e-1]" }}{PARA 6 "" 1 "" {TEXT -1 48 "[.171513472500873754e-5, 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