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RSMAMS SEAJMAMS South East Asian Journal of Mathematics and Mathematical Sciences
Home Volume 20, Issue 2 Article
Research Article

ANTI-SIMPSON'S QUADRATURE FORMULA AND ITS EXTENSION FOR EVALUATION OF ELLIPTIC AND OTHER INTEGRALS IN ADAPTIVE ENVIRONMENT

D
Debasish Das Department of Mathematics, Bhadrak Autonomous College, Bhadrak, Odisha, INDIA
S
Sanjit Kumar Mohanty Department of Mathematics, B.S. College, Jajpur - 754296, Odisha, INDIA
L
Litan Kumar Barikee Department of Mathematics, SOA University, Bhubaneswar, Odisha, INDIA
R
Rajani B. Dash Department of Mathematics, Ravenshaw University, Cuttack, Odisha, INDIA
Volume 20, Issue 2 Pages 463-476 August 30, 2024 132 downloads
Article overview

Abstract

We have constructed an anti-Simpson's quadrature formula using Simpson's $\frac{1}{3}rd$ quadrature formula following the idea given by D. P. Laurie. An extension of this formula is developed by taking average linear combination with the Simpson's $\frac{1}{3}rd$ quadrature formula. Through error analysis, we studied the theoretical dominance of this extended anti-Simpson's quadrature formula over its constituents. We accomplished numerical verification of the formula evaluating test integrals including elliptic ones. We depict the novelty of the formula in both non-adaptive and adaptive environments. In adaptive environment the dominancy of the rule over its constituents clarifies both in number of steps and error committed.

Keywords and Phrases

Simpson's $\frac{1}{3}rd$ quadrature formula $(Q_{S_{3}}(f))$Anti-Simpson's 4-point quadrature formula $(Q_{aS_{4}}(f))$Extended anti-Simpson's quadrature formula $(DS_1(f))$Adaptive integration schemeElliptic integrals.

AMS Subject Classification

Primary 65D30, 65D32, Secondary 65E05, 65A05.

Reference information

How to Cite

Debasish Das, Sanjit Kumar Mohanty, Litan Kumar Barikee, Rajani B. Dash (2024). ANTI-SIMPSON'S QUADRATURE FORMULA AND ITS EXTENSION FOR EVALUATION OF ELLIPTIC AND OTHER INTEGRALS IN ADAPTIVE ENVIRONMENT. South East Asian Journal of Mathematics and Mathematical Sciences, 20(2), 463-476.
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