The algebraic and analytic properties of the characteristic function of a linear multistep method are analyzed to provide an upper bound on the step size of a method. The step size may be chosen such that the zeros of a certain polynomial have moduli less than one. The convergence of a linear multistep method depends on a relationship between the order and the step number of the method and the location of the zeros of a certain polynomial.

(1968) Wendt, Richard Lawrence; Wiginton, C. Lamar; Decell, Henry P., Jr.; Lloyd, Justin T.; Dalton, Charles

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The laminar flow in the entrance region of a circular sector is investigated by linearizing the governing equation and considering the velocity as the fully developed velocity plus a difference velocity. The non-linear transformation is determined "after the fact" in that the axial coordinate is stretched, the problem solved in the transformed coordinate system and the "stretching factor" then determined by equating two expressions for the pressure gradient. There are no experimental results with which to compare, however, the results compare very favorably with similar analyses in a circular tube.