A New Basis Implementation for a Mixed Order Boundary Value ODE Solver

The numerical approximation of mixed order systems of multipoint value ordinary differential equations by collocation requires appropriate representation of the piecewise polynomial solutions. B-splines were originally implemented in the general purpose code COLSYS, but better alternatives exist. One promising alternative as proposed by Osborne and discussed by Ascher, Pruess and Russell. In this paper we analyze the performance of the latter solution representation for cases not previously covered, where the mesh is not necessarily dense. This analysis and other considerations have led us to implement a basis replacement in COLSYS and we discuss some implementation details. Numerical results are given which demonstrate the improvement in performance of the code.