Numerical Studies of Multichannel Variational Synthesis

Selengut observed that, by applying an appropriate variational principle to an equivalent system of first-order differential equations rather than to one higher order equation, one eliminates the restriction of the latter to continuous trial functions. This approach is particularly suited for nodal representations. Results of the new method, discussed in this paper for a set of Sturm-Liouville problems, indicate a significant improvement over more conventional variational schemes.