# Accession Number:

## AD0662009

# Title:

## AN INITIAL-VALUE METHOD FOR FREDHOLM INTEGRAL EQUATIONS WITH DEGENERATE KERNELS,

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CALIF

# Personal Author(s):

# Report Date:

## 1967-11-01

# Pagination or Media Count:

## 9.0

# Abstract:

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

# Descriptors:

# Subject Categories:

- Theoretical Mathematics