Volterra integral equation

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In mathematics, the Volterra integral equations are a special type of integral equations. They are divided into two groups referred to as the first and the second kind.

A Volterra equation of the first kind is

f(x) = \int_a^x K(x,t)\,\phi(t)\,dt.

A Volterra equation of the second kind is

\phi(x) = f(x) + \lambda \int_a^x K(x,t)\,\phi(t)\,dt.

In operator theory, and in Fredholm theory, the corresponding equations are called the Volterra operator.

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