ScienceAsia 48 (2022): 479-487 |doi:
Some new super convergence of a quartic integro-spline at
the mid-knots of a uniform partition
Feng-Gong Lang*, Xiao-Ping Xu
ABSTRACT: In this paper, we study some new super convergence of a quartic integro-spline at the mid-knots of a
uniform partition. We prove that the quartic integro-spline has super convergence in function values approximation
(sixth order convergence), in second-order derivatives approximation (fourth order convergence) and in fourth-order
derivatives approximation (second order convergence) at the mid-knots, no matter that the quartic integro-spline is
determined by using four exact boundary conditions or is determined by using four approximate boundary conditions.
These new super convergence properties also have been numerically examined.
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||School of Mathematical Sciences, Ocean University of China, Qingdao, Shandong 266100 China
* Corresponding author, E-mail: firstname.lastname@example.org
Received 29 Jun 2021, Accepted 7 Feb 2022