Authors:Umair Khalid Qureshi,Prem kumar,Feroz Shah,Kamran Nazir Memon,
Keywords:applications equations,cubic methods,open methods,convergence,results,
AbstractFinding the single root of nonlinear equations is a classical problem that arises in a practical application in Engineering, Physics, Chemistry, Biosciences, etc. For this purpose, this study traces the development of a novel numerical iterative method of an open method for solving nonlinear algebraic and transcendental application equations. The proposed numerical technique has been founded from Secant Method and Newton Raphson Method, and the proposed method is compared with the Modified Newton Method and Variant Newton Method. From the results, it is pragmatic that the developed numerical iterative method is improving iteration number and accuracy with the assessment of the existing cubic method for estimating a single root nonlinear application equation.
I. Adnan Ali Mastoi , Muhammad Mujtaba Shaikh, Abdul Wasim Shaikh. ‘A NEW THIRD-ORDER DERIVATIVE-BASED ITERATIVE METHOD FOR NONLINEAR EQUATIONS’. J. Mech. Cont.& Math. Sci., Vol.-15, No.-10, October (2020) pp 110-123. DOI : 10.26782/jmcms.2020.10.00008
II. Akram, S. and Q. U. Ann., (2015), Newton Raphson Method, International Journal of Scientific & Engineering Research, Vol. 6.
III. Allame M., and N. Azad, (2012), On Modified Newton Method for Solving a Nonlinear Algebraic Equations by Mid-Point, World Applied Sciences Journal, Vol. 17(12), pp. 1546-1548, ISSN 1818-4952 IDOSI Publications.
IV. Biswa N. D., (2012), Lecture Notes on Numerical Solution of root Finding Problems.
V. Dalquist G. and A. Bjorck, Numerical Methods in Scientiﬁc Computing, SIAM, Vol. 1 (2008).
VI. Iwetan, C. N., I. A. Fuwape, M. S. Olajide, and R. A. Adenodi, (2012), Comparative Study of the Bisection and Newton Methods in solving for Zero and Extremes of a Single-Variable Function, J. of NAMP, Vol. 21, pp. 173-176.
VII. John, H. M., An Improved Newton Raphson Method, California State University, Fullerton, Vol.10.
VIII. Kang, S. M., (2015), Improvements in Newton-Raphson Method for Non-linear Equations Using Modified Adomian Decomposition Method, International Journal of Mathematical Analysis Vol. 9.
IX. Qureshi, U. K., (2017), Modified Free Derivative Open Method for Solving Non-Linear Equations, Sindh University Research Journal, Vol.49(4), pp. 821-824.
X. Qureshi, U. K. and A. A. Shaikh, (2018), Modified Cubic Convergence Iterative Method for Estimating a Single Root of Nonlinear Equations, J. Basic. Appl. Sci. Res., Vol. 8(3) pp. 9-13.
XI. Rajput, k., A. A. Shaikh and S. Qureshi, “Comparison of Proposed and Existing Fourth Order Schemes for Solving Non-linear Equations, Asian Research Journal of Mathematics, Vol. 15, No. 2, pp.1-7, 2019.
XII. Sehrish Umar, 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. DOI : 10.26782/jmcms.2020.10.00006.
XIII. Singh, A. K., M. Kumar and A. Srivastava, (2015), A New Fifth Order Derivative Free Newton-Type Method for Solving Nonlinear Equations, Applied Mathematics & Information Sciences an International Journal,Vol.9(3), pp. 1507-1513.
XIV. Somroo, E., (2016), On the Development of a New Multi-Step Derivative Free Method to Accelerate the Convergence of Bracketing Methods for Solving, Sindh University Research Journal (Sci. Ser.) Vol. 48(3), pp. 601-604.
XV. Soram R., (2013), On the Rate of Convergence of Newton-Raphson Method, The International Journal of Engineering and Science, Vol-2, ISSN(e): 2319–1813 ISSN(p): 2319 – 1805.
XVI. Umer, S., M. M. Shaikh, A. W. 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.
XVII. Weerakoon, S. And T. G. I. Fernando, A Variant of Newton’ s Method with Accelerated Third-Order Convergence, Applied Mathematics Letters Vol. 13, pp. 87-93.