B-Spline Linear Multistep Methods and their Continuous Extensions

摘要: In this paper, starting from a sequence of results which can be traced back to I. J. Schoenberg, we analyze class spline collocation methods for the numerical solution ordinary differential equations (ODEs) with points coinciding knots. Such are naturally associated special linear multistep methods, here called B-spline (BS) able generate values at We prove that, provided additional conditions appropriately chosen, such all convergent and $A$-stable. The convergence property BS is inherited by related extensions, which, way, easily safely computable using their representation.