A Practical Method for Determining Green's Functions Using Hadamard's Variational Formula.

by H. H. Natsuyama, Robert E. Kalaba


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A method of computing Green's function as the solution of stable initial-value problems, using analog and digital computers to integrate large systems of ordinary differential equations subject to initial conditions. The solutions to many problems in mechanics, wave propagation, and mathematical physics can be represented in terms of Green's functions, but because of the difficulty of obtaining Green's functions either analytically or computationally, these representations have been viewed as theoretical rather than practical. The present method makes use of the work of Hadamard, in which the behavior of the Green's function is studied at a fixed point as a function of the length of the interval. Results of some numerical experiments are also included. 15 pp. Refs.

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