Abstract
In this paper, we modify the classical cubic B-spline quasi-interpolant by utilizing multi-node higher-order expansions and the
-exact A-discretization approach. The proposed quartic spline quasi-interpolant
possesses higher accuracy with small computational complexity increased, while requires no additional information of the target function. Applying the proposed quasi-interpolant, we develop high accuracy quadrature formulas and the differentiation matrices. All corresponding error estimates with explicit coefficients are provided. Numerical experiments illustrate the effectiveness of the proposed quasi-interpolants.
Acknowledgements
The authors appreciate the anonymous reviewers for the valuable comments that helped to improve the clarity of the manuscript.
Disclosure statement
No potential conflict of interest was reported by the author(s).