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Help me with this Partial Differential Equation

  1. Jun 10, 2013 #1
    Hi All,
    Please I need your assistance to solve this PDE below:

    [itex]\frac{\partial^2 X}{\partial t^2} - \frac{\partial^2 X}{\partial z^2} + a(z,t) \frac{\partial X}{\partial t} + b(z,t) \frac{\partial X}{\partial z} +c(z,t) X =\Phi(z,t)[/itex]

    With initial and boundary condition:
    [itex]X(z,0)=\frac{\partial X(z,0)}{\partial t}=0[/itex]
    [itex]X(0,t)=X(L,t)=0[/itex]

    Thank you in advance.
    FM
     
  2. jcsd
  3. Jun 10, 2013 #2
    Are you trying to solve an equation like this analytically or numerically? Solving it numerically isn't too difficult, but solving it analytically is.
     
  4. Jun 10, 2013 #3
    Thank you for your response. I want to solve it analytically

     
  5. Jun 10, 2013 #4

    berkeman

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    Staff: Mentor

    What is this equation from? Is this for schoolwork, or research, or other?
     
  6. Jun 10, 2013 #5
    It's research

     
  7. Jun 10, 2013 #6

    SteamKing

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    Staff Emeritus
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    Homework Helper

    If it's research, shouldn't you be doing some of the research?
     
  8. Jun 10, 2013 #7

    dextercioby

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    Homework Helper

    Doing some (not too in depth) reasearch in the field of solving PDE's doesn't leave with too many options to try to find a solution. The method of characteristics or separating variables should be the first ones you should try. Whether a (preferably closed form and expressible in terms of known special functions) solution can be found is directly dependent on the fact that the 4 coefficient functions have a 'nice', i.e. preferable constant form, so that the PDE would have the smallest possible non-linearity (even though, as written, it's classifield as linear).

    Either way, your best research is done with a smart computer software such as Mathematica.
     
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