Quadratic/linear rational spline collocation for linear boundary value problems

We investigate the collocation method with quadratic/linear rational spline S of smoothness class C-2 for the numerical solution of two-point boundary value problems if the solution y (or - y) of the boundary value problem is a strictly convex function. We show that on the uniform mesh it holds parallel to S - y parallel to(infinity)= O(h(2)). Established bound of error gives a dependence on the solution of the boundary value problem and its coefficient functions. We prove also convergence rates parallel to S' - y'parallel to(infinity) = O (h(2)) and parallel to S '' - y ''parallel to(infinity) = O (h(2)). Numerical examples support the obtained theoretical results. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.