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 [2]), 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 cot θ(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 singleand 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].