On a new computational solution of time-dependent processes-I: a one-dimensional case.

by Richard Ernest Bellman, Robert E. Kalaba, M. C. Prestrud

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A discussion of the transformation of linear functional equations subject to boundary conditions into nonlinear functional equations subject only to initial conditions in space and time coordinates. The approach of invariant imbedding yields the reflected and transmitted fluxes as functions of basic physical dimensions. The computational treatment of the reflection of plane parallel flux form an infinite plane medium of finite thickness has already been determined for the steady state-case. As a first step toward the computational solution of the corresponding problem for the time-dependent case, this paper studies the reflected flux from a one-dimensional rod for the case of neutron transport. To obtain a numerical solution, the problem of inverting the Laplace transform numerically is investigated. The method used is quite simple and is applicable to more general problems.

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