Re: Mathematica Question - Using DSolve with Boundary Conditions

*To*: mathgroup at smc.vnet.net*Subject*: [mg97532] Re: Mathematica Question - Using DSolve with Boundary Conditions*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Sat, 14 Mar 2009 18:15:47 -0500 (EST)*References*: <gpg1aj$cft$1@smc.vnet.net>

Hi, write a function, that solve your problem and rename it to DSolve[], because DSolve[] build in Mathematica can't solve this kind of problems. Regards Jens James Huth wrote: > Dear Mathgroup: > > I am trying to reproduce the analytic solution to a pair of partial > differential equations subject to boundary conditions. The analytic > solution has been published in an older journal article - I am trying to > reproduce/ verify/ understand the solution. > > I believe I have set up DSolve correctly. However, when the line is > executed DSolve simply returns the equations and boundary conditions rather > than solving the system. > > Notes: > * There are two partial differential equations, two unknown variables, and > three boundary conditions. > * The second and third boundary conditions are supposed to hold when: WN, > WA and the partial derivatives of WN , WA with respect to t are evaluated > at the value t == ts, where ts is an arbitrary constant. > * Arbitrary constants include: a, b, d, e, k, r, s > > I would like to solve for WN and WA which are both functions of [t, m]. > > Here is the code I tried: > > DSolve[{-t m + (b e - d m) D[WN[t, m], m] + a t D[WN[t, m], t] + 1/2 s^2 > t^2 D[WN[t, m], t, t] == r WN[t, m], > -t m - d m D[WA[t, m], m] + a t D[WA[t, m], t] + 1/2 s^2 t^2 D[WA[t, m], t, > t] == r WA[t, m], > WN[0, m] == 0, WN[ts, m] == WA[ts, m] - k, D[WN[ts,m],t] == D[WA[ts,m],t]}, > {WN[t, m], WA[t, m]}, {t, m}] > > OR... > > DSolve[{-t m + (b e - d m) D[WN[t, m], m] + a t D[WN[t, m], t] + 1/2 s^2 > t^2 D[WN[t, m], t, t] == r WN[t, m], > -t m - d m D[WA[t, m], m] + a t D[WA[t, m], t] + 1/2 s^2 t^2 D[WA[t, m], t, > t] == r WA[t, m], > WN[0, m] == 0, WN[ts, m] == WA[ts, m] - k, (D[WN[t,m],t]/.t->ts) == > (D[WA[t,m],t]/.t->ts)}, {WN[t, m], WA[t, m]}, {t, m}] > > > The published solution is of the form (where A and y are positive constants > to be determined): > > WN[t, m] = A t^y - t m / (r + d - a) - b e t / ((r - a) (r + d - a)) > > WA[t, m] = - t m / (r + d - a) > > Can anyone advise how to use DSolve to yield solutions for WN and WA? > > Sincerely, > > James Huth > jh288507 at ohio.edu > >