The method of characteristics has been used in a variety of graphical, analytical, and numerical ways as a powerful tool in the solution of hyperbolic partial differential equations. The availability of digital computers permits the basic method to be applied to a greatly extended class of problems represented by semihyperbolic equations. This general extension is illustrated by problems of unsteady fluid flow in rigid tubes with the effects of frequency or history-dependent wall shear and heat transfer.
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F. T. Brown (1969) studied this question.