Derivative based two-point Gauss Legendre rule for the Riemann-Stieltjes integral
P. M. Mohanty1, S.N. Mohapatra2, M. Acharya3
1P. M. Mohanty, Department of Mathematics, Siksha Anusandhan Deemed University, Bhubaneswar, India.
2S. N. Mohapatra, Department of Mathematics, Siksha Anusandhan Deemed University, Bhubaneswar, India.
3M. Acharya, Department of Mathematics, Siksha Anusandhan Deemed University, Bhubaneswar, India.
Manuscript received on 20 June 2019 | Revised Manuscript received on 27 June 2019 | Manuscript Published on 22 June 2019 | PP: 345-348 | Volume-8 Issue-8S2 June 2019 | Retrieval Number: H10630688S219/19©BEIESP
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: In this paper, derivative based two point Gauss-Legendre rule for the Riemann-Stieltjes integral is presented which uses derivative value in order to approximate the Riemann-Stieltjes integral 1-1∫ƒ(t) d g (t). This integral rule increases the order of the precision over the two point Gauss-Legendre rule meant for the Riemann-Stieltjes integration and the error term for the approximation is investigated.
Keywords: Riemann- Stieltjes Integral, Gauss Two Point Rule, Error Term.
Scope of the Article: Cryptography and Applied Mathematics