A Stable Version of the Modified Algorithm for Error Minimization in Combined Numerical Integration | [Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences • 2023]

Author(s):

1. Aijaz Bhatti: Institution of Mathematics and Computer Science, University of Sindh,Jamshoro,Pakistan

2. Owais Ali Rajput: Institution of Mathematics and Computer Science, University of Sindh,Jamshoro,Pakistan

3. Zubair Ahmed Kalhoro: Institution of Mathematics and Computer Science, University of Sindh,Jamshoro,Pakistan

Abstract:

The present study derives a stable version of “A Modified Algorithm for Reduction of Error in Combined Numerical Integration”. It is discovered that the earlier proposed scheme “A Modified Algorithm for Error Reduction in Combined Numerical Integration” exhibits accuracy fluctuations when the number of slits, n, is increased (n = 9). . Starting with the number of slits n = 9 and increasing the count of sub-intervals, the error increases spontaneously. This spontaneous spike in error is resolved by considering a better combination of quadrature rules. To this, the notable result of this study is the identification of an optimal choice for quadrature formulae that could minimizes error lfuctuations in combined numerical integration regardless the number of slits ( n). With this revised choice, the error remains relatively stable and predictable even as the count of sub-intervals is increased.

Page(s): 37-43

DOI: 10.53560/PPASA(60-2)813

Published: Journal: Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, Volume: 60, Issue: 2, Year: 2023

Keywords:

Simpsons 13 rule , Weddles Rule , numerical integration , SixPoint Rule , Booles Rule

References:

[1] Gordon K.S. .1998 .Numerical integration. Encyclopedia of Biostatistics ISBN: 0471975761, : .

[2] M.M. Shaikh M.S.,Chandio M.S.,Soomro A.S. . .A modified Four-point Closed Mid-point Derivative Based Quadrature Rule for Numerical Integration. , : .

[3] .2016 .. , 48(2) : 389-392.

[4] Dukkipati R.V. .2010 .. Numerical methods. New Age International Publisher ISBN 10: 8122428134, ISBN, 13 : 368.

[5] Karpagam A.,Vijayalakshmi V. .2018 .Comparison Results of Trapezoidal, Simpson's 1/3 rule, Simpson's 3/8 rule and Weddle's rule. Asian Journal of Mathematical Sciences, 2(4) : 50-53.

[6] Amanat M. .2015 .Numerical Integration and a Proposed Rule. American Journal of Engineering Research, 4 : 120-123.

[7] Natarajan A.,Mohankumar N. .1995 .A comparison of some quadrature methods for approximating Cauchy principal value integrals. Journal of Computational Physics, 116(2) : 365-368.

[8] Liu D.J.,J.M. Wu D.H.,Yu D.H. .2010 .The Super Convergence Of The Newton-Cotes Rule For Cauchy Principal Value Integrals. Journal of Bhatti et al Computational and Applied Mathematics, 235(3) : 696-707.

[9] GM . .. aanndd AM. S.M..SoSomhariok, : .

[10] . .2A(n2a0l1y6si)s. of polynomial collocation and uniformly spaced quadrature methods for 3. oVn.d Dkuiknkdiplaintie.arNuFmreedrhicoallm minetthegordasl. eNqeuwatioAngse -InatecronmatpioanriaslonP.uTbulriskhisehr JIoSuBrNnal 1o0f: A8n1a2ly2s4i2s8a1n3d4, NIuSmBbNer13T:h9e7o8ry8172(42), 3260819(2) : 29811-3917.

[11] Sa . .. KBahrpaattgi, : .

[12] .2019 .SRheasikuhlt.s AoMfoTdirfieadpeAzoligdoarli,thmSi mfoprsoRne'sduc1ti/o3n roufle, ESrirmorpsionn'Csom3/b8inerduleNuamndericWaledIdnltee'gsratriuolne.. SAinsdiahn UJnoiuvrenrasiltyoRfesMeaartchhemJoautircnaall (SScciieenncceesSe2ri(e4s. , 7(4250-1785) : 0.

[13] Beyer W.H. . .. CRC Standard Mathematical Tables., : .

[14] . .A1n2a0l-y1s2is3. (M20c1G5r)a. ohankumar. A comparison N., : .

[15] Ro . .. Dth.odsFafiorers.appNrouxmimeraitcianlg dCifearuecnhtiyatiopnrincip&al valiunetegirnatteiognrals. nJuomurenraiclal of dCifeormenptuiattaitoino.nalNPuhmyesricicsa1l1a6n(a2l)y:s3is651-7346-188, (29051) : 1.

[16] Amjad A.,Hamayun F.,Muhammad U. . .. , : .

[17] - ,- ,-n3- C .2010 .Rule For Cauchy Principal Value Integrals. Journal of Computational and Applied Mathematics, 235(3) : 696-707.

Citations

Downloads

Views