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Integral Equations curiosity question

  1. Jan 27, 2016 #1
    Hello, i'm getting interest in the name integral equations and what it can give to me of insights, but i don't see any application of this, can anyone give me a example where it is used??
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  3. Jan 27, 2016 #2


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    Just like differential equations, where the change in a certain quantity w.r.t. time for example, is used to model certain phenomena, integral equations are used where the processes involved are expressed with integrals rather than derivatives.


    Integral equations are found commonly in potential theory, electrostatics and electrodynamics, fluid mechanics, etc.
  4. Jan 28, 2016 #3


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    This is a nice question.

    In addition to being used directly for modeling purposes, integral equations (IEs) also arise quite frequently in a more indirect and "hidden" way, namely as reformulations of problems involving differential equations (DEs). In this context, linear initial value problems for DEs lead to so-called Volterra IEs (variable limits of integration) while linear boundary value problems give rise to Fredholm IEs (fixed limits of integration). One advantage of such a reformulation is that the behavior of integral operators is usually much better from an analytical and numerical point of view than the behavior of the original differential operators.

    Shortly, I hope to post elsewhere on this site a simple example that will hopefully illustrate the relationship between periodic solutions of a nonlinear DE, a boundary value problem and a certain type of nonlinear integral equation.
  5. Jan 28, 2016 #4
    Thanks for the answers!!, and Krylov i will wait for your post about it :)
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