(*^ ::[ Information = "This is a Mathematica Notebook file. It contains ASCII text, and can be transferred by email, ftp, or other text-file transfer utility. It should be read or edited using a copy of Mathematica or MathReader. If you received this as email, use your mail application or copy/paste to save everything from the line containing (*^ down to the line containing ^*) into a plain text file. On some systems you may have to give the file a name ending with ".ma" to allow Mathematica to recognize it as a Notebook. 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<-- ********************************************************* Current Values for Unknowns ********************************************************* b1 x ¶ : a = a00 + a01 t + ---- x 3 ¶ : b = b0 + b1 t t 2 b1 u ¶ : f = -a01 - ------ u 3 ********************************************************* a00 is constant a01 is constant b0 is constant b1 is constant ********************************************************* :[font = output; output; inactive; preserveAspect; endGroup] {42.4*Second, Null} ;[o] {42.4 Second, Null} :[font = input; preserveAspect; startGroup] hkdv = (ut == uxxx + uxx + u ux) :[font = output; output; inactive; preserveAspect; endGroup] dd[t][u] == u*dd[x][u] + dd[x, x][u] + dd[x, x, x][u] ;[o] u == u u + u + u t x xx xxx :[font = input; preserveAspect; startGroup] SolveDetEq[hkdv]//Timing :[font = print; inactive; preserveAspect] --> Differential Equations Solved! <-- ********************************************************* Current Values for Unknowns ********************************************************* ¶ : a = a00 + a01 t x ¶ : b = b t ¶ : f = -a01 u ********************************************************* a00 is constant a01 is constant b is constant ********************************************************* :[font = output; output; inactive; preserveAspect; endGroup] {53.25*Second, Null} ;[o] {53.25 Second, Null} :[font = input; preserveAspect; startGroup] beq = (utt == uxxxx + dx[dx[u^2]]) :[font = output; output; inactive; preserveAspect; endGroup] dd[t, t][u] == 2*dd[x][u]^2 + 2*u*dd[x, x][u] + dd[x, x, x, x][u] ;[o] 2 u == 2 u + 2 u u + u tt x xx xxxx :[font = input; preserveAspect; startGroup] SolveDetEq[beq]//Timing :[font = print; inactive; preserveAspect] --> Differential Equations Solved! <-- ********************************************************* Current Values for Unknowns ********************************************************* b1 x ¶ : a = a0 + ---- x 2 ¶ : b = b0 + b1 t t ¶ : f = -(b1 u) u ********************************************************* a0 is constant b0 is constant b1 is constant ********************************************************* :[font = output; output; inactive; preserveAspect; endGroup] {157.3*Second, Null} ;[o] {157.3 Second, Null} :[font = input; preserveAspect; startGroup] kg = uxt == u^2 :[font = output; output; inactive; preserveAspect; endGroup] dd[t, x][u] == u^2 ;[o] 2 u == u tx :[font = input; preserveAspect; startGroup] SolveDetEq[kg] :[font = print; inactive; preserveAspect; endGroup] --> Differential Equations Solved! <-- ********************************************************* Current Values for Unknowns ********************************************************* ¶ : a = a0 + a1 x x ¶ : b = b0 + b1 t t ¶ : f = -(a1 u) - b1 u u ********************************************************* a0 is constant a1 is constant b0 is constant b1 is constant ********************************************************* :[font = input; preserveAspect; startGroup] he = (ut == uxx) :[font = output; output; inactive; preserveAspect; endGroup] dd[t][u] == dd[x, x][u] ;[o] u == u t xx :[font = input; preserveAspect; startGroup] SolveDetEq[he] :[font = print; inactive; preserveAspect; endGroup] Current Differential Equations ********************************************************* -b + 2 a0 t x -a0 - 2 f1 + a0 t x xx f0 - f0 t xx f1 - f1 t xx ********************************************************* Current Values for Unknowns ********************************************************* ¶ : a = a0 x ¶ : b = b t ¶ : f = f0 + f1 u u ********************************************************* a0 depends on {x, t} b depends on {t} f0 depends on {x, t} f1 depends on {x, t} ********************************************************* :[font = input; preserveAspect; startGroup] SolveDiff :[font = print; inactive; preserveAspect; endGroup] Current Differential Equations ********************************************************* x b tt -a00 - 2 f1 - ----- t x 2 f0 - f0 t xx -b tt ---- - 2 f1 2 xx f1 - f1 t xx x b ttt -a00 - 2 f1 - ------ tt tx 2 f0 - f0 tt txx f1 - f1 tt txx f0 - f0 tx xxx f1 - f1 tx xxx ********************************************************* Current Values for Unknowns ********************************************************* x b t ¶ : a = a00 + ---- x 2 ¶ : b = b t ¶ : f = f0 + f1 u u ********************************************************* a00 depends on {t} b depends on {t} f0 depends on {x, t} f1 depends on {x, t} ********************************************************* :[font = input; preserveAspect; startGroup] SolveDiff :[font = print; inactive; preserveAspect; endGroup] Current Differential Equations ********************************************************* f0 - f0 t xx f0 - f0 tt txx f0 - f0 tx xxx f0 - f0 ttt ttxx f0 - f0 ttx txxx f0 - f0 txx xxxx ********************************************************* Current Values for Unknowns ********************************************************* b1 x ¶ : a = a000 - 2 f11 t + ---- - 2 f101 t x x 2 2 ¶ : b = b0 + b1 t - 2 f101 t t 2 f101 u x ¶ : f = f0 + f100 u + f101 t u + f11 u x + --------- u 2 ********************************************************* a000 is constant b0 is constant b1 is constant f0 depends on {x, t} f100 is constant f101 is constant f11 is constant ********************************************************* :[font = input; preserveAspect] quickjet[2,2,2] :[font = input; preserveAspect; startGroup] nls = {ut == -vxx - (u^2 + v^2) v, vt == uxx + (u^2 + v^2) u} :[font = output; output; inactive; preserveAspect; endGroup] {dd[t][u] == -(v*(u^2 + v^2)) - dd[x, x][v], dd[t][v] == u*(u^2 + v^2) + dd[x, x][u]} ;[o] 2 2 2 2 {u == -(v (u + v )) - v , v == u (u + v ) + u } t xx t xx :[font = input; preserveAspect; startGroup] SolveDetEq[nls]//Timing :[font = print; inactive; preserveAspect] Current Differential Equations ********************************************************* x b tt -a0 - 2 f01 - ----- t x 2 -b tt ---- - f01 2 xx ********************************************************* Current Values for Unknowns ********************************************************* x b t ¶ : a = a0 + ---- x 2 ¶ : b = b t u b t ¶ : f = f01 v - ---- u 2 v b t ¶ : g = -(f01 u) - ---- v 2 ********************************************************* a0 depends on {t} b depends on {t} f01 depends on {x} ********************************************************* :[font = output; output; inactive; preserveAspect; endGroup] {101.7166666666666668*Second, Null} ;[o] {101.717 Second, Null} :[font = input; preserveAspect; startGroup] SolveDiff //Timing :[font = print; inactive; preserveAspect] --> Differential Equations Solved! <-- ********************************************************* Current Values for Unknowns ********************************************************* b1 x ¶ : a = a00 - 2 f011 t + ---- x 2 ¶ : b = b0 + b1 t t -(b1 u) ¶ : f = ------- + f010 v + f011 v x u 2 b1 v ¶ : g = -(f010 u) - ---- - f011 u x v 2 ********************************************************* a00 is constant b0 is constant b1 is constant f010 is constant f011 is constant ********************************************************* :[font = output; output; inactive; preserveAspect; endGroup] {2.166666666666667851*Second, Null} ;[o] {2.16667 Second, Null} :[font = input; preserveAspect; startGroup] bs = {ut == u ux + vx - uxx, vt == dx[u v] + vxx} :[font = output; output; inactive; preserveAspect; endGroup] {dd[t][u] == u*dd[x][u] + dd[x][v] - dd[x, x][u], dd[t][v] == v*dd[x][u] + u*dd[x][v] + dd[x, x][v]} ;[o] {u == u u + v - u , v == v u + u v + v } t x x xx t x x xx :[font = input; preserveAspect; startGroup] SolveDetEq[bs]//Timing :[font = print; inactive; preserveAspect] --> Differential Equations Solved! <-- ********************************************************* Current Values for Unknowns ********************************************************* b1 x ¶ : a = a00 + a01 t + ---- x 2 ¶ : b = b0 + b1 t t b1 u ¶ : f = -a01 - ---- u 2 ¶ : g = -(b1 v) v ********************************************************* a00 is constant a01 is constant b0 is constant b1 is constant ********************************************************* :[font = output; output; inactive; preserveAspect; endGroup] {98.90000000000000036*Second, Null} ;[o] {98.9 Second, Null} :[font = input; preserveAspect] quickjet[3,1,4] :[font = input; preserveAspect; startGroup] kp = uyy == dx[ut - uxxx - u ux] :[font = output; output; inactive; preserveAspect; endGroup] dd[y, y][u] == -dd[x][u]^2 + dd[t, x][u] - u*dd[x, x][u] - dd[x, x, x, x][u] ;[o] 2 u == -u + u - u u - u yy x tx xx xxxx :[font = input; preserveAspect; startGroup] SolveDetEq[kp]//Timing :[font = print; inactive; preserveAspect] Current Differential Equations ********************************************************* 2 y b tt c0 - 2 a0 + ------- t y 3 b tt --- - a0 3 yy b ttt ---- - a0 3 tyy ********************************************************* Current Values for Unknowns ********************************************************* x b t ¶ : a = a0 + ---- x 3 ¶ : b = b t 2 y b t ¶ : c = c0 + ------ y 3 2 u b x b t tt ¶ : f = -a0 - ------ - ----- u t 3 3 ********************************************************* a0 depends on {t, y} b depends on {t} c0 depends on {t} ********************************************************* :[font = output; output; inactive; preserveAspect; endGroup] {263.7666666666666657*Second, Null} ;[o] {263.767 Second, Null} :[font = input; preserveAspect; startGroup] SolveDiff//Timing :[font = print; inactive; preserveAspect] --> Differential Equations Solved! <-- ********************************************************* Current Values for Unknowns ********************************************************* 2 x b y c0 y b t t tt ¶ : a = a00 + ---- + ----- + ------ x 3 2 6 ¶ : b = b t 2 y b t ¶ : c = c0 + ------ y 3 2 2 u b x b y c0 y b t tt tt ttt ¶ : f = -a00 - ------ - ----- - ------ - ------- u t 3 3 2 6 ********************************************************* a00 depends on {t} b depends on {t} c0 depends on {t} ********************************************************* :[font = output; output; inactive; preserveAspect; endGroup] {60.73333333333333428*Second, Null} ;[o] {60.7333 Second, Null} ^*)