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

by J. L. Casti, H. H. Natsuyama, Robert E. Kalaba


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A computer program for the solution of a Fredholm integral equation of the second kind with a displacement kernel is given. The Fredholm integral equation is transformed into an initial-value problem by treating the interval length as the independent variable. The method of reduction is invariant imbedding. The numerical integration is accomplished by using a fourth-order Adams-Moulton predictor-corrector method, with a fourth-order Runge-Kutta method to start the process. The program was used to solve the basic integral equation of radiative transfer, and results were compared with those obtained by Sobolev, by Viskanta, by Bellman, Kagiwada, and Kalaba, and by Heaslet and Warming. Results were in excellent agreement. 43 pp. Refs. (See also RM-5186, RM-5556.) (MW)

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