Integral Equations curiosity question

[Andreol263]

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??

 

[SteamKing]

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??

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.

https://en.wikipedia.org/wiki/Integral_equation

Integral equations are found commonly in potential theory, electrostatics and electrodynamics, fluid mechanics, etc.

 

[S.G. Janssens]

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.

 

[Andreol263]

Thanks for the answers!, and Krylov i will wait for your post about it :)