tailieunhanh - Adaptive quadrature method to approximate double integrals over non rectangular regions
In that paper, even the algorithm was constructed strictly for approximating double integrals over rectangles only, it can be also extended to treat the case of non-rectangular regions. Nevertheless, for nonrectangular regions, it is not somewhat practical to program such an algorithm because of the consumption a large amount of RAM to store data of values for functions taking on the boundary of the region. | Phạm Thị Thu Hằng và Đtg Tạp chí KHOA HỌC & CÔNG NGHỆ 181(05): 179 - 183 ADAPTIVE QUADRATURE METHOD TO APPROXIMATE DOUBLE INTEGRALS OVER NON-RECTANGULAR REGIONS Pham Thi Thu Hang, Dinh Van Tiep* University of Technology - TNU ABSTRACT Recently, in an early publication [1], the author presented an algorithm to approximate double integral over a rectangle basing on the adaptive quadrature method. This method has the upper hand comparing with many other approaches due to its low cost and high efficiency. In that paper, even the algorithm was constructed strictly for approximating double integrals over rectangles only, it can be also extended to treat the case of non-rectangular regions. Nevertheless, for nonrectangular regions, it is not somewhat practical to program such an algorithm because of the consumption a large amount of RAM to store data of values for functions taking on the boundary of the region. The storage is performed at many steps in each repeating loop. This shortcoming often makes the program implement awkwardly. This paper aims to revise the aforementioned algorithm to be more efficient. Key words: numerical integration, approximate double integral, adaptive method, adaptive quadrature, non-rectangle region. INTRODUCTION* Similar to an algorithm for the adaptive quadrature of double integrals over a rectangular region, presented in [1], one of double integral over general regions, or more exactly, over non-rectangular regions, could be constructed. Here, we confine the consideration to such regions bounded by graphs of functions, Ω = .
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