An Initial-Value Method for Fredholm Integral Equations with Degenerate Kernels

摘要

The final step in the mathematical treatment of many problems in such fields as radiative transfer, neutron transport, and optimal filtering theory involves the solution of a Fredholm integral equation in which the kernel is degenerate or can be closely approximated by a degenerate kernel. The standard procedure for solving such an equation is to convert it into an equivalent matrix equation and compute the solution by evaluating a number of integrals and performing a matrix inversion. This last step, however, can present serious computational difficulties. In this study, invariant imbedding techniques are used to convert the Fredholm equation into an initial-value problem, and the troublesome matrix inversion is replaced in this formulation by solving a Riccati system of differential equations. (Author)