Re: Simple PDE with side conditions

*To*: mathgroup at smc.vnet.net*Subject*: [mg115486] Re: Simple PDE with side conditions*From*: Oliver Ruebenkoenig <ruebenko at wolfram.com>*Date*: Wed, 12 Jan 2011 04:07:59 -0500 (EST)

On Tue, 11 Jan 2011, schochet123 wrote: > "NDSolve" was a misprint for "DSolve". Sorry. > > What about with DSolve in version 8? > > Steve Nope, not out of the box. Oliver > > > On Jan 11, 1:59 pm, Oliver Ruebenkoenig <ruebe... at wolfram.com> wrote: >> On Tue, 11 Jan 2011, schochet123 wrote: >>> Unfortunately, Mathematica cannot solve this (yet?). >> >>> Note that the functional equation is not needed since the solution is >>> determined by the PDE plus the initial condition. >> >>> However, at least in version 7, NDSolve does not seem to solve >>> first-order PDEs in three independent variables. Even the "trivial" >>> problem >> >> You can solve this with NDSolve in version 7: >> >> L = 4; >> sol = NDSolve[{ >> D[u[t, x, y], t] + D[u[t, x, y], x] == 0 >> , u[t, -L, y] == u[t, L, y] >> , u[t, x, -L] == u[t, x, L] >> , u[0, x, y] == Exp[-(x^2 + y^2)] >> }, u, {t, 0, 1}, {x, -L, L}, {y, -L, L}] >> >> Manipulate[ >> Plot3D[u[t, x, y] /. First[sol], {x, -L, L}, {y, -L, L}, >> PlotRange -> All], {t, 0, 1}] >> >> >> >>> DSolve[{D[u[t, x, y], t] + D[u[t, x, y], x] == 0, >>> u[0, x, y] == 0}, u, {t, x, y}] >> >>> does not get solved, although if you remove all the appearances of ",y" it is solved. >> >>> Can someone with version 8 check if there have been any improvements in that version? >> > >