Cover: Direct and Inverse Problems for Integral Equations via Initial-Value Methods.

Direct and Inverse Problems for Integral Equations via Initial-Value Methods.

Published 1967

by H. H. Natsuyama, Robert E. Kalaba

Purchase Print Copy

 Format Price
Add to Cart Paperback-245 pages $20.00

A numerical scheme for solving integral equations which exploits the capability of modern computers to integrate systems of several hundred or several thousand simultaneous ordinary differential equations subject to known initial conditions. The scheme is based on the conversion of a basic integral equation of transport theory into initial-value problems. Inverse problems, which involve estimating properties of the sources of the radiation field and the medium, given certain observations on the solution of the radiation field, are viewed as nonlinear multipoint boundary-value problems that can be solved numerically by a quasilinearization technique. Results of numerical experiments are included, as well as numerous references to other works on the subject. The study should be of particular interest to meteorologists, physicists, and numerical analysts. 39 pp. Refs.

This report is part of the RAND research memorandum series. The Research Memorandum was a product of RAND from 1948 to 1973 that represented 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

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.