Deprived of Second Derivative Iterated Method for Solving Nonlinear Equations
Second Derivative Iterated Method for Solving Non-linear Equations
DOI:
https://doi.org/10.53560/PPASA(58-2)605Keywords:
Taylor Series Expansion, Newton Method, Modified Newton Method, Order of ConvergenceAbstract
Non-linear equations are one of the most important and useful problems, which arises in a varied collection of practical applications in engineering and applied sciences. For this purpose, in this paper has been developed an iterative method with deprived of second derivative for the solution of non-linear problems. The developed deprived of second derivative iterative method is convergent quadratically, and which is derived from Newton Raphson Method and Taylor series. The numerical results of the developed method are compared with the Newton Raphson Method and Modified Newton Raphson Method. From graphical representation and numerical results, it has been observed that the deprived of second derivative iterative method is more appropriate and suitable as accuracy and iteration perception by the valuation of Newton Raphson Method and Modified Newton Raphson Method for estimating a non-linear problem.
References
N.D. Biswa, Lecture Notes on Numerical Solution of root Finding Problems (2012).
C.N. Iwetan, I.A. Fuwape, M.S. Olajide, and R.A. Adenodi, Comparative Study of the Bisection and Newton Methods in solving for Zero and Extremes of a Single-Variable Function, J. of NAMP, Vol. 21, 173-176, (2012).
J.C. Ehiwario, S.O. Aghamie, Investigation of different strategies for finding root, IOSR Journal of Engineering, Vol. 04, 6, 01-07 (2014).
A.A. Siyal, A.A. Shaikh, A.H. Shaikh, “Hybrid Closed Algorithm for Solving Non-linear Equations in one Variable”, Sindh Univ. Res. Jour., Vol. 48(4), 779-782, (2016)
A.A. Sangah, A.A. Shaikh and S.F. Shah, Comparative Study of Existing Bracketing Methods with Modified Bracketing Algorithm for solving Non-linear Equations in single variable, Sindh University Research Journal, Vol: 48(1), (2016).
A.A. Siyal, R.A. Memon, N.M. Katbar, and F. Ahmad, Modified Algorithm for Solving Non-linear Equations in Single Variable, J. Appl. Environ. Biol. Sci., 7(5), 166-171, (2017).
E. Soomro, On the Development of a New Multi- Step Derivative Free Method to Accelerate the Convergence of Bracketing Methods for Solving, Sindh University Research Journal, Vol. 48(3), 601- 604 (2016).
K. Jisheng, Y. Li and X. Wang, on modified Newton methods with cubic convergence, Applied Mathematics and Computation, 176, 123-127, (2006).
U.K. Qureshi, Modified Free Derivative Open Method for Solving Non-Linear Equations, Sindh University Research Journal, Vol. 49 (4), 821-824 (2017).
U.K. Qureshi, M.Y. Ansari, M.R. Syed 2018, Super Linear Iterated Method for Solving Non- Linear Equations, Newton Raphson Method, Sindh University Research Journal, Vol.: 50(1), 137-140, (2018).
R. Soram, S. Roy, S.R. Singh, M. Khomdram, S. Yaikhom and S. Takhellambam, On the Rate of Convergence of Newton-Raphson Method, The International Journal of Engineering and Science, Vol:2 (11), (2013).
N.A. Din, Some New Type Iterative Methods for Solving Nonlinear Algebraic Equation, World Appl. Sci. J., 26 (10), 1330-1334 (2013).
H.M. John, An Improved Newton-Raphson Method, California State University, Fullerton, CA 92634, vol 10.
