An Initial-value Method for Fredholm Integral Equations with Degenerate Kernels.
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. 8 pp. Refs.
- Format:
- Paperback
- Year:
- 1967
- List Price:
- $20.00
- Price:
- $16.00 Special 20% Web Discount
Document Details
- Copyright: RAND Corporation
- Availability: Available
- Format:
- List Price: Free
- Document Number: RM-5516-PR
- Year: 1967
- Series: Research Memoranda
This report is part of the RAND Corporation research memorandum series. The Research Memorandum was a product of the RAND Corporation from 1948 to 1973 that represented working papers meant to report current results of RAND research to appropriate audiences.
The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.
RAND® is a registered trademark. Copyright © 1994-2012 RAND Corporation.