Results 1 to 6 of 6

Math Help - partial differential equation with mathematica

  1. #1
    Junior Member
    Joined
    May 2013
    From
    Canada
    Posts
    37
    Thanks
    3

    partial differential equation with mathematica

    Hi,

    i tried to solve the following viscous diffusion equation using mathematica , but it did not come up with a solution:

    the equation is D(u(y,t))/Dt=v D^2(u(y,t))/Dy^2

    conditions:

    t=0 u(y,0)=0
    y=0 u(0,t)=c
    y=inf u(inf,t)=0

    The mathematica statement i used is :

    DSolve[{D[u[y, t], {t, 1}] - v D[u[y, t], {y, 2}] == 0, u[0, t] == 0,
    u[y, 0] == c, u[y, \[Infinity]] == 0}, u[y, t], {y, t}]


    Any help with getting the right solution using mathematica?

    Thanks

    mopen
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,381
    Thanks
    918

    Re: partial differential equation with mathematica

    I can see some problems with what you've got.

    First off one of your boundary conditions is incorrectly specified.

    You say that $u(\infty,t)=0$ but you've entered it as $u(y, \infty)=0$

    Second your boundary and initial conditions aren't consistent at (0,0).

    One boundary condition says $u(0,0)=c$ the initial condition says $u(0,0)=0$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,381
    Thanks
    918

    Re: partial differential equation with mathematica

    From a tutorial on using DSolve.

    "The heat equation is parabolic, but it is not considered here because it has a nonvanishing nonprincipal
    part, and the algorithm used by DSolve is not applicable in this case."


    The diffusion equation is of the same form as the heat equation. It doesn't look like DSolve is designed to solve this. NDSolve can be used though if you have a number for v.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    May 2013
    From
    Canada
    Posts
    37
    Thanks
    3

    Re: partial differential equation with mathematica

    Ok, how to solve it using NDSOLVE , if v=1e-5 , y=0--10, t=0--30, c=5.

    Thanks
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,381
    Thanks
    918

    Re: partial differential equation with mathematica

    Quote Originally Posted by mopen80 View Post
    Ok, how to solve it using NDSOLVE , if v=1e-5 , y=0--10, t=0--30, c=5.

    Thanks
    i don't know how to interpret what you've written above. I don't think you fixed the inconsistent boundary values problem either.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,520
    Thanks
    1405

    Re: partial differential equation with mathematica

    Couldn't you set $\displaystyle \begin{align*} u(y,t) = Y(y)T(t) \end{align*}$ and apply separation of variables?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Partial Differential Equation
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: January 29th 2011, 06:20 PM
  2. Differential equation mathematica
    Posted in the Math Software Forum
    Replies: 2
    Last Post: November 2nd 2010, 05:57 AM
  3. Partial differential equation-wave equation - dimensional analysis
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: August 28th 2009, 11:39 AM
  4. Replies: 0
    Last Post: April 16th 2009, 07:23 AM
  5. Graphing a differential equation in mathematica?
    Posted in the Math Software Forum
    Replies: 0
    Last Post: April 7th 2009, 08:10 PM

Search Tags


/mathhelpforum @mathhelpforum