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A Generalized Quartic Quadrature Based Adaptive Scheme

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Abstract

In this paper we successfully developed a quadrature rule \(SR_{4b} (f)\) of increased precision. In the process we combined four quadrature rules of lower precision using a non-conventional generalized approach. The new rule so formed is termed as quartic quadrature. We presented the generalized approach which is capable of combining a bunch of quadrature rules of lower precisions to produce a generalized quadrature of higher precision. We analysed the truncation error of the new rule \(SR_{4b} (f)\). We also compared the error estimate of this rule with those of its four ingredient quadratures. We found that the rule \(SR_{4b} (f)\) is theoretically dominating its ingredients. We used this rule as base rule in an adaptive integration scheme. We took some line integrals of analytic functions as test integrals. We obtained highly encouraging results by numerically evaluating the test integrals in both non adaptive and adaptive mode using the new formula \(SR_{4b}(f)\).

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Authors and Affiliations

  1. Department of Mathematics, B.S Degree College, Jajpur, 754296, Odisha, India

    Sanjit Kumar Mohanty

  2. Department of Mathematics, Ravenshaw University, Cuttack, 753003, Odisha, India

    Rajani Ballav Dash

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  1. Sanjit Kumar Mohanty
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  2. Rajani Ballav Dash
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Correspondence to Sanjit Kumar Mohanty.

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Mohanty, S.K., Dash, R.B. A Generalized Quartic Quadrature Based Adaptive Scheme. Int. J. Appl. Comput. Math 8, 191 (2022). https://doi.org/10.1007/s40819-022-01405-2

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  • DOI: https://doi.org/10.1007/s40819-022-01405-2

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