On numerical solution of multiparameter Sturm-Liouville spectral problems
The method proposed here has been devised for solution of the spectral problem for the Lamé wave equation (see ), but extended lately to more general problems. This method is based on the phase function concept or the Prüfer angle determined by the Prüfer transformation cotθ(x) = y'(x)/y(x), where y(x) is a solution of a second order self-adjoint o.d.e. The Prüfer angle θ(x) has some useful properties very often being referred to in theoretical research concerning both single- and multi-parameter Sturm-Liouville spectral problems (see e.g. [6,14,5]). All these properties may be useful for numerical solution of the above problems as well. For an account of numerical methods for solving the single-parameter Sturm-Liouville spectral problem by means of a modified Prüfer transformation one is referred to [1,11,9].
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