An Initial-value Method for General Fredholm Integral Equations.

Harriett H. Natsuyama, Robert E. Kalaba, Alan Schumitzky

ResearchPublished 1967

A new analytical and numerical solution of Fredholm integral equations is presented that is not limited, as previously, to equations whose kernels depend on the absolute value of the difference of the arguments. The solution of a Fredholm integral equation at a fixed point is viewed as a function of the length of the interval. An initial-value problem for the solution and for certain auxiliary quantities is then derived (an extension of invariant imbedding), and a number of new equations are developed that are well suited for solution by modern computers. This procedure for the computation of the solution is also of analytic interest: it has been tested and found to be effective in dealing with equations of radiative transfer. 17 pp. Refs. (See also RM-5186-PR, RM-5258-PR, RM-5306-PR.)

Document Details

Citation

Chicago Manual of Style

Natsuyama, Harriett H., Robert E. Kalaba, and Alan Schumitzky, An Initial-value Method for General Fredholm Integral Equations. Santa Monica, CA: RAND Corporation, 1967. https://www.rand.org/pubs/research_memoranda/RM5307.html.
BibTeX RIS

This publication is part of the RAND research memorandum series. The research memorandum series, a product of RAND from 1948 to 1973, included working papers meant to report current results of RAND research to appropriate audiences.

This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.

RAND 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.