Category:Definitions/Volterra Integral Equations

This category contains definitions related to Volterra Integral Equations.
Related results can be found in Category:Volterra Integral Equations.

The Volterra integral equations are integral equations of the first and second kind such that the limits of integration are between a constant $a$ and the variable $x$:

Volterra Integral Equation of the First Kind

A Volterra integral equation of the first kind is an integral equation of the form:

$\ds \map f x = \lambda \int_a^x \map K {x, y} \map g y \rd y$

where $g$ is an unknown real function.

Volterra Integral Equation of the Second Kind

A Volterra integral equation of the second kind is an integral equation of the form:

$\ds \map g x = \map f x + \lambda \int_a^x \map K {x, y} \map g y \rd y$

where $g$ is an unknown real function.

Source of Name

This entry was named for Samuel Giuseppe Vito Volterra.