Pseudo-spectral derivative of quadratic quasi-interpolant splines

Abstract

In this paper we consider the problem of approximating the derivative of a function $f$ in a certain interval $[a,b]$. We propose a local method based on the approximation of the derivative of $f$ by the derivative of a quadratic $C^1$ spline quasi-interpolant $Q_2f$, introduced by Sablonni\`ere. Differentiating $Q_2f$ we construct the pseudo-spectral derivative at the quasi-interpolation knots and the corresponding differentiation matrix. An error analysis is proposed and some numerical results are given.