A Proposal for the Calculation of Characteristic Functions for Certain Differential and Integral Operators via Initial-Value Procedures.

by J. L. Casti, Robert E. Kalaba, M. Douglas Scott

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The theory of invariant imbedding gives the solution of an inhomogeneous problem in terms of the solution to an initial-value problem. This memorandum presents a computational approach for the solution of an inhomogeneous Fredholm integral equation of the form u = Tu + f. This equation and an expansion formula of classical analysis allow a proposal to be made for calculating the solutions to a corresponding homogeneous equation. The proposal developed here is of interest for its ability to produce isolated characteristic functions; the determination of characteristic values is applicable to neutron multiplication and is equivalent to obtaining critical dimensions of nuclear reactors. Discussion includes possible numerical difficulties and extension to other types of linear operators. 28 pp. Ref. (KB)

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