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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.Gör. Ali YILDIRIM
>> Gaziantep Ã?niversitesi
>> Nizip Meslek Yüksekokulu
>> Gıda Teknolojisi Programı
>> 27700-Nizip-Gaziantep/Türkiye
>> 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
> 


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