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

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

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

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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.

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