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Research articles

ScienceAsia 48 (2022): 479-487 |doi: 10.2306/scienceasia1513-1874.2022.063


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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a School of Mathematical Sciences, Ocean University of China, Qingdao, Shandong 266100 China

* Corresponding author, E-mail: fenggonglang@sina.com

Received 29 Jun 2021, Accepted 7 Feb 2022