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Re: diff equation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg88333] Re: diff equation
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Fri, 2 May 2008 03:42:12 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <BLU129-DS335A7C6B4ED0F214741F6A8D90@phx.gbl> <4818FDAB.60005@gmail.com> <fvc5v1$9ks$1@smc.vnet.net>

Ali YILDIRIM wrote:

> [resent a more readable form - moderator]
> 
>  Dear Math group..
> 
>  I have an differential equation. I can not solve in mathematica.
>  Would you help me, please?
> 
>   dM/d t =D[d^2 M//dr^2 +(2/r) (dM/dr)]-kM
-----------!!!----!!!!
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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