Differential Systems for Eigenvalues of Fredholm Integral Equations.

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

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The practical computational solution of nonhomogeneous Fredholm integral equations is extended to the eigenvalue problem for homogeneous integral equations. The eigenvalues and eigenfunctions are viewed at a fixed point as functions of the interval length. A complete set of ordinary differential equations is derived from these and other related quantities. Analogous systems of equations are developed for displacement kernels and Green's functions. Certain problems concerning the initial conditions remain. Two methods to circumvent this obstacle are discussed. 21 pp. Ref. (See also RM-5076, RM-5186, RM-5258, RM-5286.)

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