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Volterra equations

  1. Oct 2, 2011 #1
    Hi Guys!
    I have a (stupid) question. In which physical phenomena do you use Volterra equations (or similar equations) ?
    I mean if we go back to traditional heat,diffusion,wave, transport... and so on we know more or less when to use them. Are integral equation just a dual representation or is there a specific reason to use them ?
    Thanx
    Alex
     
  2. jcsd
  3. Oct 2, 2011 #2
    A differential equation:

    [tex]
    y' = f(x, y)
    [/tex]

    with the initial condition [itex]y(x_{0}) = y_{0}[/itex] is equivalent to the integral equation:

    [tex]
    y(x) = y_{0} + \int_{x_{0}}^{x}{f(t, y(t)) \, dt}
    [/tex]

    This is a Volterra (since the upper bound of the integral is variable) integral equation of the second kind (since the unknown function [itex]y(x)[/itex] is both under the integral and outside).
     
  4. Oct 2, 2011 #3
    Probably my question was not clear. I didn't ask for a definition (everybody can look up wikipedia), I asked when do you need to use them ?
    some inverse problem... for example ? I am asking when did you meet them, in which phenomena ?
     
    Last edited: Oct 2, 2011
  5. Oct 2, 2011 #4
    Is what I typed a definition?
     
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