Splines and Collocation for Ordinary Initial Value Problems

Normally, the methods for solving ordinary initial value problems are viewed as discrete algorithms. However, a subclass of these schemes can be constructed by aiming at a global continuous approximation to the unknown solution. In this paper we approximate the solution by a spline of degree m and continuity k, 0 ≤ k ≤ m - 1. In each subinterval the m - k free parameters are determined by collocation. The choice of collocation points is discussed with respect to zero-stability, superconvergence and A-stability.

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