Mathematica Question - Using DSolve with Boundary Conditions

*To*: mathgroup at smc.vnet.net*Subject*: [mg97477] Mathematica Question - Using DSolve with Boundary Conditions*From*: James Huth <jh288507 at ohio.edu>*Date*: Sat, 14 Mar 2009 05:36:12 -0500 (EST)

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