Umair Khalid Qureshi,Sanaullah Jamali,Zubair Ahmed Kalhoro,Abdul Ghafoor Shaikh,



Boole Rule and Weddle Rule,convergence criteria,existing methods,graph,results,


This article is presented a modified quadrature iterated methods of Boole rule and Weddle rule for solving non-linear equations which arise in applied sciences and engineering. The proposed methods are converged quadratically and the idea of developed research comes from Boole rule and Weddle rule. Few examples are demonstrated to justify the proposed method as the assessment of the newton raphson method, steffensen method, trapezoidal method, and quadrature method. Numerical results and graphical representations of modified quadrature iterated methods are examined with C++ and EXCEL. The observation from numerical results that the proposed modified quadrature iterated methods are performance good and well executed as the comparison of existing methods for solving non-linear equations.


I. Akram, A. and Q. U. Ann, Newton Raphson Method, International Journal of Scientific & Engineering Research, Vol. 6. 456-462, 2015.
II. Khatri, A., A. A. Shaikh and K. A. Abro, Closed Newton Cotes Quadrature Rules with Derivatives, ,, Vol.9, No.5, 2019.
III. Liu, Z. and H. Zhang, Steffensen-Type Method of super third-order convergence for solving nonlinear equations, Journal of Applied Mathematics and Physics, vol 2, 581-586, 2014.
IV. Memon Kashif, Muhammad Mujtaba Shaikh, Muhammad Saleem Chandio, Abdul Wasim Shaikh, : A NEW AND EFFICIENT SIMPSON’S 1/3-TYPE QUADRATURE RULE FOR RIEMANN-STIELTJES INTEGRAL, J. Mech. Cont. & Math. Sci., Vol.-15, No.-11, November (2020) pp 132-148
V. Perhiyar, M. A., S. F. Shah and A. A. Shaikh, Modified Trapezoidal Rule Based Different Averages for Numerical Integration, Mathematical Theory and Modeling, Vol.9, No.9, 2019.
VI. Qureshi, U. K., A New Accelerated Third-Order Two-Step Iterative Method for Solving Nonlinear Equations, Mathematical Theory and Modeling, Vol: 8(5), 2018.
VII. Qureshi, U. K., I. A. Bozdar, A. Pirzada and M. B. Arain, Quadrature Rule Based Iterative Method for the Solution of Non-Linear Equations, Proceedings of the Pakistan Academy of Sciences, Pakistan Academy of Sciences A. Physical and Computational Sciences, vol: 56 (1): 39–43, 2019.
VIII. Qureshi, U. K., Z. A. Kalhoro, A. A. Shaikh and A. R. Nagraj, Trapezoidal Second Order Iterated Method for Solving Nonlinear Problems, University of Sindh Journal of Information and Communication Technology (USJICT), Vol: 2(2), 2018.
IX. Shaikh, M. M., M. S. Chandio and A. S. Soomro, A Modified Four-point Closed Mid-point Derivative Based Quadrature Rule for Numerical Integration, Sindh University Research Journal, SURJ (Science Series), 48(2), 2016.
X. Umar Sehrish , Muhammad Mujtaba Shaikh , Abdul Wasim Shaikh, : A NEW QUADRATURE-BASED ITERATIVE METHOD FOR SCALAR NONLINEAR EQUATIONS, J. Mech. Cont.& Math. Sci., Vol.-15, No.-10, October (2020) pp 79-93.
XI. Weerakoon, S. and T. G. I. Fernando, 2000, A Variant of Newton’ s Method with Accelerated Third-Order Convergence, Applied Mathematics Letters, vol 13 87-93.
XII. Zafar, F., Saira S. and C. O. E. Burg, New Derivative Based Open Newton-Cotes Quadrature Rules, Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2014.
XIII. Zhao, W. and L. Hongxing, Midpoint Derivative-Based Closed Newton-Cotes Quadrature, Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2013.

View Download