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How to solve the following (integro-differential eq.)

  1. Mar 17, 2009 #1
    Hi all,

    I'm struggeling with an equation of the following form:

    [tex]\frac{\partial A\left(x,t\right)}{\partial t} = \int_{x_0}^{x_1} f\left(x,x',t\right)A\left(x',t\right) dx'[/tex]

    The problem is defined on the interval [tex]x_0 \leq x \leq x_1[/tex], where [tex]f\left(x,x',t\right)[/tex] is a known function. We have the initial condition [tex]A\left(x,0\right) = g\left(x\right)[/tex].

    For my specific problem I found the qualitative behavior of the solution [tex]A\left(x,t\right)[/tex] by straightforward numerical integration. But I would like to be able to find analytic solutions... Any suggestions on how to proceed here?
    Any help is very much appreciated!! :smile:
     
    Last edited: Mar 17, 2009
  2. jcsd
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