Differentiation Based on Optimal Local SplineQuasi-Interpolants with Applications

摘要

In this paper we propose a method for the approximation of the derivative of a function f based on discrete local optimal spline quasi-interpolants Qk of degree k = 3,4,5. By differentiating Qkf, we construct the approximation of the derivative at the quasi-interpolation nodes and the corresponding differentiation matrices. Some numerical results and applications to univariate boundary-value problems are given.