Quadratic/linear rational spline collocation for linear boundary value problems

We investigate the collocation method with quadratic/linear rational spline S of smoothness class C2 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 ‖S−y‖∞=O(h2). Established bound of error gives a dependence on the solution of the boundary value problem and its coefficient functions. We prove also convergence rates ‖S′−y′‖∞=O(h2) and ‖S″−y″‖∞=O(h2). Numerical examples support the obtained theoretical results.