integral transform (redirected from Kernel (integral equation))

integral transform

In mathematics, a function that results when a given function is multiplied by a so-called kernel function, and the product is integrated (see integration) between suitable limits. Its value lies in its ability to simplify intractable differential equations (subject to particular boundary conditions) by transforming the derivatives and boundary conditions into terms of an algebraic equation that may easily be solved. The solution yielded must be converted to the final solution using an inverse transformation. Several integral transforms are named for the mathematicians who introduced them (Fourier transform, Laplace transform).