The Invariant Imbedding Numerical Method for Fredholm Integral Equations with Degenerate Kernels.

by H. H. Natsuyama, Robert E. Kalaba, B. J. Vereeke


Purchase Print Copy

 FormatList Price Price
Add to Cart Paperback-245 pages $20.00 $16.00 20% Web Discount

Application of invariant imbedding in deriving an initial-value method for solving Fredholm integral equations with degenerate kernels. By regarding the solution at a fixed point as a function of the interval of integration, a differential equation is obtained; this equation, combined with knowledge of the solution for one interval length, makes it possible to determine the solution for other lengths. The principal advantage of the initial-value formulation is its ease of resolution by modern digital and analog computers. Emphasis is on the inhomogeneous problem, although some remarks on the eigenvalue problem are included. A FORTRAN program for solving the initial-value problem is also given, with subroutines written for an Adams-Moulton integration scheme with a Runge-Kutta start. 39 pp. Refs.

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.

Our mission to help improve policy and decisionmaking through research and analysis is enabled through our core values of quality and objectivity and our unwavering commitment to the highest level of integrity and ethical behavior. To help ensure our research and analysis are rigorous, objective, and nonpartisan, we subject our research publications to a robust and exacting quality-assurance process; avoid both the appearance and reality of financial and other conflicts of interest through staff training, project screening, and a policy of mandatory disclosure; and pursue transparency in our research engagements through our commitment to the open publication of our research findings and recommendations, disclosure of the source of funding of published research, and policies to ensure intellectual independence. For more information, visit

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.