Title: A generalised quadrature of order four for analytic functions

Authors: Sanjit Kumar Mohanty; Rajani Ballav Dash

Addresses: Department of Mathematics, B.S. Degree College, Jajpur, Odisha, 754296, India ' Department of Mathematics, Ravenshaw University, Cuttack, Odisha, 753003, India

Abstract: This paper introduces a novel approach to formulating n-rule combinations departing from traditional mixing up of rules, which is termed as generalised quadrature method. In this process, a bunch of quadrature rules of lower precisions are mixed to form a generalised quadrature rule of higher precision. We stated the conditions for forming the generalised quadrature and derived from its truncation error. Using the generalised approach, we formulate a quadrature rule SR_4a(f) of order four and precision eleven by using; Booles, Gauss-Legendre 3-point, Clenshaw-Curtis 7-point and Kronrod extension of Lobatto 4-point rules. The truncation error associated with SR_4a(f) is analysed and compared with those of the constituent rules and found to be the least. We verify the dominance of SR_4a(f) by numerically evaluating some test integrals. We also verify that the generalised quadrature gives a better result than the constituent rules when applied in adaptive environment.

Keywords: generalised quadrature rule; SR-conditions; order of generalised quadrature rule; SR_4a(f); ESR_4a(f).

DOI: 10.1504/IJCSM.2024.137846

International Journal of Computing Science and Mathematics, 2024 Vol.19 No.3, pp.285 - 298

Accepted: 31 Oct 2023
Published online: 05 Apr 2024 *

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