Numerical Integration Based on Bivariate Quartic Quasi-Interpolation Operators

Renhong Wang 1, Xiaolei Zhang 2*

1 Institute of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
2 Institute of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China/ Department of Applied Mathematics, Changchun University of Science and Technology, Changchun 130022, China

Received October 17, 2006; Accepted (in revised version) November 8, 2006
Abstract

In this paper, we propose a method to deal with numerical integral by using two kinds of $C^2$ quasi-interpolation operators on the bivariate spline space, and also discuss the convergence properties and error estimates. Moreover, the proposed method is applied to the numerical evaluation of 2-D singular integrals. Numerical experiments will be carried out and the results will be compared with some previously published results.

Key words: $S_4^2(\Delta_{mn}^{(2)})$; quasi-interpolation operators; singular integrals.

AMS subject classifications: 65D32, 65D30, 41A15

Correspondence to: Xiaolei Zhang , Institute of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China Email: zhangxl0411@yahoo.com.cn