An Initial-Value Theory for Fredholm Integral Equations with Semidegenerate Kernels

摘要

An initial-value method for solving Fredholm integral equations having a kernel with one degenerate form in one region and another degenerate form in another region. Fredholm equations having kernels of the type considered here are of particular interest because of their pertinence to the solution of two-point boundary problems. When such a problem is reformulated as an integral equation, the kernel is a Green's function having one form in one region and another form in another region. The Green's function may be first determined and then approximated to the desired degree of accuracy by a semidegenerate kernel. Volterra equations are also considered as a special case, and some discussion of critical lengths and eigenvalues is provided. (Author)