A generalised quadrature of order four for analytic functions Online publication date: Fri, 05-Apr-2024
by Sanjit Kumar Mohanty; Rajani Ballav Dash
International Journal of Computing Science and Mathematics (IJCSM), Vol. 19, No. 3, 2024
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 SR4a(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 SR4a(f) is analysed and compared with those of the constituent rules and found to be the least. We verify the dominance of SR4a(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.
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