THEMATIC PROGRAMS

Over the past three decades, methods based on orthogonal spline collocation (OSC) - spline collocation at Gauss points - have evolved as effective techniques for the solution of boundary value problems for ordinary and partial differential equations, and in the method of lines solution of initial-boundary value problems. These methods have several attractive features such as their high order global accuracy and superconvergence properties, and ease of implementation. In this talk, we provide an overview of recent developments in the formulation and analysis of OSC methods for partial differential equations. Special attention is devoted to methods for certain second and fourth order elliptic boundary value problems and to efficient techniques for the solution of the associated systems of linear algebraic equations. We also discuss discrete-time OSC methods for Schrodinger systems in two space variables which arise in vibration problems.