
Accession Number : AD0662009
Title : AN INITIALVALUE 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 initialvalue 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