Re: partial differential equation of diffusion

*To*: mathgroup at smc.vnet.net*Subject*: [mg88341] Re: partial differential equation of diffusion*From*: "Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com>*Date*: Fri, 2 May 2008 03:43:38 -0400 (EDT)*References*: <BLU129-DS716E7490C4367AC35F1EEA8DB0@phx.gbl>

On Thu, May 1, 2008 at 10:28 PM, Ali YILDIRIM <ayildirim10 at hotmail.com> wrote: > > > > Dear Jeanmarch Gulliet, > > When I was clear my equation, the resulting one is bellow. > > > > dM/d t =a[d^2 M//dr^2 +(2/r) (dM/dr)]-kM > > The differentials are partial differentials. > > a and k are constants. > > > >Could you write now, please? [Note that it is better to ask/post questions directly to MathGroup rather than to send it to a specific person.] 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