Institution: | Applied & Computational Mathematics Group, School of Electrical Engineering and Science, Faculty of Military Science, Technology and Management, Royal Military College of Science, Cranfield Institute of Technology, Shrivenham, Swindon, Wilts SN6 8LA, United Kingdom |
Abstract: | Significant advances have been made in the last year or two in algorithms and theory for Sturm—Liouville problems (SLPs). For the classical regular or singular SLP ?(p(x)u′)′ + q(x)u = λw(x)u, a < x < b, we outline the algorithmic approaches of the recent library codes and what they can now routinely achieve. For a library code, automatic treatment of singular problems is a must. New results are presented which clarify the effect of various numerical methods of handling a singular endpoint. For the vector generalization ?(P(x)u′)′+Q(x)u = λW(x)u where now u is a vector function of x, and P, Q, W are matrices, and for the corresponding higher-order vector self-adjoint problem, we outline the equally impressive advances in algorithms and theory. |