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I have been encountered an integral equation that I need to solve\evaluate numericly and I didn't find anything like it in my search yet.

The equation:

\frac{d^2 F(t)}{dt^2}=const*\int_{t'}\frac{sin(F(t)-F(t'))}{(t-t')^{2k}}dt'

If it helps there is a specific case, when K=1 there is an analitical solution: F(t)=2arctan(\frac{t}{t_0}).

For now, two mainly things will help me:

1: What is the exact name of category of this integral equation?

2: What is the name of the numerical solution that solve it, or solve something similar to this equation and where should I start looking?

Thank you

Ofek

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# Numerical solution for an integral equation?

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