A double series variational method for a class of second kind Fredholm integral equations
In an earlier paper [J. Math. Anal. Appl. 143, No. 1, 264-289 (1989; Zbl 0683.65113)] the author studied a double series variational method for solving a class of first-kind Fredholm integral equations with nondegenerate kernels. This approach is now extended to Fredholm integral equations of the second kind, by formally rewriting the given equation as a first-kind equation, \[ \lambda^{-1}[f(v)- g(v)]= \int^ b_ a K(v,x)f(x)dx. \] Computationally, the method appears to be more expensive than comparable Galerkin or collocation methods but improved accuracy and convergence characteristics, as well as additional flexibility of implementation may make this drawback less serious. There are, however, no numerical results to illustrate these aspects.
Fredholm integral equations of the second kind
scientific article; zbMATH DE number 636041