Accession Number : AD0662009

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

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Kagiwada,H. H. ; Kalaba,R. E. ; Schumitzky,A. ; Ueno,S.

Report Date : NOV 1967

Pagination or Media Count : 9

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 :   (*INTEGRAL EQUATIONS, *BOUNDARY VALUE PROBLEMS), MATRICES(MATHEMATICS), DIFFERENTIAL EQUATIONS, ALGORITHMS, PROBLEM SOLVING, NEUTRON TRANSPORT THEORY, HEAT TRANSFER

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE