ALGORITHM-704 - ABDPACK AND ABBPACK-FORTRAN PROGRAMS FOR THE SOLUTION OF ALMOST BLOCK DIAGONAL LINEAR-SYSTEMS ARISING IN SPLINE COLLOCATION AT GAUSSIAN POINTS WITH MONOMIAL BASIS FUNCTIONS

ABDPACK is a package of FORTRAN programs for the solution of systems of linear equations with the almost block diagonal structure arising in spline collocation at Gaussian points with monomial spline basis functions, when applied to two-point boundary value problems with separated boundary conditions. The package ABBPACK is designed to handle a subclass of such linear systems which have what may be called an almost block bidiagonal structure. Such systems result, for example, when condensation is applied to the full spline collocation linear system. This package may also be used to solve the almost block bidiagonal systems arising in multiple shooting techniques and implicit Runge-Kutta methods for solving two-point boundary value problems. The algorithms implemented in the package are based on an alternate column and row pivoting scheme which avoids most of the fill-in introduced by more commonly used techniques.