Definition:Volterra Integral Equation
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Definition
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.
Also known as
The Volterra integral equations can also be seen in the form Volterra's integral equations.
Also see
- Results about Volterra integral equations can be found here.
Source of Name
This entry was named for Samuel Giuseppe Vito Volterra.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): integral equation
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Volterra's integral equations
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): integral equation
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Volterra's integral equations