Solving two-point boundary value problems by means of deficient quartic splines

摘要

We consider a (0, 2) lacunary interpolation problem, with prescribed nonlinear endpoint conditions, solving it in the class of quartic splines of deficiency 2. Under suitable assumptions, we show existence and uniqueness of the solution. We provide a convergence analysis, showing that the method is of order four. These results are then applied to a two-point boundary value problem. If the latter is solved with sufficiently high accuracy, we show that the smoothing method based on the first part of the paper is fourth-order accurate.