A collocation/quadrature-based Sturm-Liouville problem solver

We present a computational method for solving a class of boundary-value pro blems in Sturm-Liouville form. The algorithms are based on global polynomia l collocation methods and produce discrete representations of the eigenfunc tions. Error control is performed by evaluating the eigenvalue problem resi duals generated when the eigenfunctions are interpolated to a finer discret ization grid; eigenfunctions that produce residuals exceeding an infinity-n orm bound are discarded. Because the computational approach involves the ge neration of quadrature weights and arrays for discrete differentiation oper ations, our computational methods provide a convenient framework for solvin g boundary-value problems by eigenfunction expansion and other projection m ethods. (C) 2000 Elsevier Science Inc. All rights reserved.