integral equation
integral equation Any equation for an unknown function f(x), a←x←b, involving integrals of the function. An equation of the form
is a Volterra equation of the second kind. The analogous equation with constant limits
is a Fredholm equation of the second kind. If the required function only appears under the integral sign it is a Volterra or Fredholm equation of the first kind; these are more difficult to treat both theoretically and numerically. The Volterra equation can be regarded as a particular case of the Fredholm equation where K(x,y) = 0 for y > x
Fredholm equations of the second kind occur commonly in boundary-value problems in mathematical physics. Numerical techniques proceed by replacing the integral with a rule for numerical integration, leading to a set of linear algebraic equations determining approximations to f(x) at a set of points in a←x←b.
is a Volterra equation of the second kind. The analogous equation with constant limits
is a Fredholm equation of the second kind. If the required function only appears under the integral sign it is a Volterra or Fredholm equation of the first kind; these are more difficult to treat both theoretically and numerically. The Volterra equation can be regarded as a particular case of the Fredholm equation where K(x,y) = 0 for y > x
Fredholm equations of the second kind occur commonly in boundary-value problems in mathematical physics. Numerical techniques proceed by replacing the integral with a rule for numerical integration, leading to a set of linear algebraic equations determining approximations to f(x) at a set of points in a←x←b.
More From encyclopedia.com
Domain , Domain
The domain of a relation is the set that contains all the first elements, x, from the ordered pairs (x,y) that make up the relation. In mathem… Function , A function is a mathematical relationship between two sets of real numbers. These sets of numbers are related to each other by a rule that assigns ea… George Boole , Boole, George
Boole, George
(b. Lioncoln, England, 1815; d. Cork, Ireland, 1864)
mathematics.
George Boole was the son of John Boole, a cobbler whose… Integral , The integral is one of two main concepts embodied in the branch of mathematics known as calculus. Interpreted graphically, an integral of a function… Diophantus Of Alexandria , Diophantus of Alexandria
Diophantus of Alexandria
(fl. ad. 250)
mathematics.
We know virtually nothing about the life of Diophantus. The dating of hi… Sonya Kovalevsky , mathematics.
Sonya Kovalevsky was the greatest woman mathe. matician prior to the twentieth century. She was the daughter of Vasily Korvin-Krukovsky,…
You Might Also Like
NEARBY TERMS
integral equation