Definition:Fredholm Integral Equation

Definition

The Fredholm integral equations are integral equations of the first and second kind such that the limits of integration are constant:

Fredholm Integral Equation of the First Kind

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

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

where $g$ is an unknown real function.

Fredholm Integral Equation of the Second Kind

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

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

Also known as

The Fredholm integral equations can also be seen in the form Fredholm's integral equations.

Also see

• Results about Fredholm integral equations can be found here.

Source of Name

This entry was named for Erik Ivar Fredholm.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Fredholm's integral equations
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): integral equation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Fredholm's integral equations
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): integral equation