Re: partial differential equation of diffusion

*To*: mathgroup at smc.vnet.net*Subject*: [mg88377] Re: partial differential equation of diffusion*From*: "Ali YILDIRIM" <ayildirim10 at hotmail.com>*Date*: Sat, 3 May 2008 06:17:34 -0400 (EDT)*References*: <BLU129-DS716E7490C4367AC35F1EEA8DB0@phx.gbl> <22d35c5a0805012309s10c21a53me6a645fcb0be5a64@mail.gmail.com>

Dear Jean Marc Gulliet, >>When I put my equation as D[M[r, t], t] == a*(D[M[r, t], r, r] + >>(2/r)*D[M[r, t], r]) - k*M[r, t] in to mathematica >and initial and boundary condition as M[r, 0] == M0, D[M[0, t], t] == 0, >M[R, t] == Ms >It can not solve. The mathematica notebook is given in attachment. >Best regards > > dM/d t =a[d^2 M//dr^2 +(2/r) (dM/dr)]-kM >> > The differentials are partial differentials. >> > a and k are constants. >>> >> > Do you mean that you do not know how to multiply expressions with > Mathematica? If this is the case you should familiarize yourself with > the basis of Mathematica syntax, this will really help you and be a > time saver in the future. > > D[M[r, t], t] == > a*(D[M[r, t], r, r] + (2/r)*D[M[r, t], r]) - k*M[r, t] > >> >Best Regards.. >> > >> > >> Ã?Ä?r.GÃ¶r. Ali YILDIRIM >> Gaziantep Ã?niversitesi >> Nizip Meslek YÃ¼ksekokulu >> GÄ±da Teknolojisi ProgramÄ± >> 27700-Nizip-Gaziantep/TÃ¼rkiye >> ayildirim at gantep.edu.tr >> > -----------!!!----!!!! >> > Not sure for what this D stands here. I discarded it in the example >> > below. Also you have a spurious backslash. So you could write your >> > equation as >> > >> > D[M[r, t], t] == D[M[r, t], r, r] + 2/r D[M[r, t], r] - k M[r, t] >> > >> >> Boundary conditions are: >> >> >> >> 1-) at t=0, M= Mo >> > >> > M[r, 0] == M0 >> > >> >> 2-) r = 0, dM/dr=0 >> > >> > D[M[0, t], t] == 0 >> > >> >> 3-) at r = R, M = Ms >> > >> > M[R, t] == Ms >> > >> > Then you can use DSolve or NDSolve as in >> > >> > DSolve[{D[M[r, t], t] == >> > D[M[r, t], r, r] + 2/r D[M[r, t], r] - k M[r, t], M[r, 0] == M0, >> > D[M[0, t], t] == 0, M[R, t] == Ms}, M, {r, t}] >> > >> >> >> > > > Regards, > -- Jean-Marc >