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On the solution of a complex eigenvalue problem of Sturm-Liouville type and application to periodic internal turbulent flow. (English) Zbl 0739.76067

The authors consider the one-dimensional problem of transient forced convection in internal flow subjected to periodically varying thermal disturbances. Since it is known that its formal solution can be given as an integral transform which involves the eigenvalues and eigenfunctions of a complex eigenvalue problem, the aim of the paper is to give a procedure to compute numerically these eigenvalues and its corresponding eigenfunctions. This computation is carried out by means of a shooting method. The IVPs involved in the application of the shooting method are solved with the classical fourth order Runge-Kutta method. Some comments on the selection of starting values for the eigenvalues in the application of the shooting method are given. The paper ends with an example in which the values of the first twenty eigenvalues are computed.
Reviewer: M.Calvo (Zaragoza)

MSC:

76R05 Forced convection
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
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