A Novel Two Point Optimal Derivative free Method for Numerical Solution of Nonlinear Algebraic, Transcendental Equations and Application Problems using Weight Function

Authors

  • Sanaullah Jamali Institute of Mathematics and Computer Science, University of Sindh, Jamshoro, Sindh-Pakistan
  • Zubair Ahmed Kalhoro Institute of Mathematics and Computer Science, University of Sindh, Jamshoro, Sindh-Pakistan
  • Abdul Wasim Shaikh Institute of Mathematics and Computer Science, University of Sindh, Jamshoro, Sindh-Pakistan
  • Muhammad Saleem Chandio Institute of Mathematics and Computer Science, University of Sindh, Jamshoro, Sindh-Pakistan
  • Sanaullah Dehraj Department of Mathematics and Statistics, Quaid-e-Awam University of Engineering, Science and Technology, 67480, Nawabshah, Sindh-Pakistan

DOI:

https://doi.org/10.21015/vtm.v10i2.1288

Abstract

It’s a big challenge for researchers to locate the root of nonlinear equations with minimum cost, lot of methods are already exist in  literature to find root but their cost are very high In this regard we introduce a two-step  fourth order method by using weight function. And proposed method is optimal and derivative free for solution of nonlinear algebraic and transcendental and application problems. MATLAB, Mathematica and Maple software are used to solve the convergence and numerical problems of proposed and their counterpart methods.

References

A. M. Ostrowski. Solution of Equations in Euclidean and Banach Spaces. Academic Press, London, 1973.

A. Cordero, J. L. Hueso, E. Martínez, and J. R. Torregrosa. Steffensen type methods for solving nonlin-

ear equations. Journal of computational and applied mathematics, 236(12):3058–3064, 2012.

Z. Xiaojian. Modified chebyshev–halley methods free from second derivative. Applied mathematics

and computation, 203(2):824–827, 2008.

H. T. Kung and J. F. Traub. Optimal order of one-point and multipoint iteration. Journal of the ACM

(JACM), 21(4):643–651, 1974.

A. Cordero, J. L. Hueso, E. Martínez, and J. R. Torregrosa. Generating optimal derivative free itera-

tive methods for nonlinear equations by using polynomial interpolation. Mathematical and Computer

Modelling, 57(7-8):1950–1956, 2013.

F. Soleymani. Letter to the editor regarding the article by khattri: derivative free algorithm for solving

nonlinear equations. Computing, 95(2):159–162, 2013.

S. Jamali, Z. A. Kalhoro, A. W. Shaikh, and M. S. Chandio. A New Second Order Derivative Free Method

for Numerical Solution of Non-Linear Algebraic and Transcendental Equations using Interpolation

Technique. Journal of Mechanics of Continua Mathematical Sciences, 16(4):75–84, apr 2021. ISSN 09738975.

doi: https://doi.org/10.26782/jmcms.2021.04.00006.

S. Jamali, Z. A. Kalhoro, A. W. Shaikh, and M. S. Chandio. An Iterative, Bracketing & Derivative-Free

Method for Numerical Solution of Non-Linear Equations using Stirling Interpolation Technique. Journal

of Mechanics of Continua Mathematical Sciences, 16(6):13–27, jun 2021. ISSN 0973-8975. doi:

https://doi.org/10.26782/jmcms.2021.06.00002.

A. Cordero and J. R. Torregrosa. Low-complexity root-finding iteration functions with no derivatives

of any order of convergence. Journal of Computational and Applied Mathematics, 275:502–515, 2015.

B. Neta. A new derivative-free method to solve nonlinear equations. Mathematics, 9:6, 2021.

I. K. Argyros, M. Kansal, V. Kanwar, and S. Bajaj. Higher-order derivative-free families of chebyshev–

halley type methods with or without memory for solving nonlinear equations. Applied Mathematics

and Computation, 315:224–245, 2017.

A. Suhadolnik. Combined bracketing methods for solving nonlinear equations. Applied Mathematics

Letters, 25(11):1755–1760, 2012.

A. Suhadolnik. Superlinear bracketing method for solving nonlinear equations. Applied Mathematics

and Computation, 219(14):7369–7376, 2013.

Wajid Shaikh, Abdul Shaikh, Muhammad Memon, and Abdul Sheikh. Convergence rate for the hybrid

iterative technique to explore the real root of nonlinear problems. Mehran University Research Journal

of Engineering and Technology, 42(1), 2023. doi: https://doi.org/10.22581/muet1982.2301.16.

W. A. Shaikh, A. G. Shaikh, M. Memon, A. H. Sheikh, and A. A. Shaikh. Numerical Hybrid Iterative

Technique for Solving Nonlinear Equations in One Variable. Journal of Mechanics of Continua and

Mathematical Sciences, 16(7):57–66, 2021. ISSN 0973-8975. doi: https://doi.org/10.26782/jmcms.2021.0

00005.

P. Sivakumar and J. Jayaraman. Some new higher order weighted newton methods for solving nonlinear

equation with applications. Mathematical and Computational Applications, 24:2, 2019.

C. Chun, B. Neta, J. Kozdon, and M. Scott. Choosing weight functions in iterative methods for simple

roots. Applied Mathematics and Computation, 227:788–800, 2014.

Q. Zheng, J. Li, and F. Huang. An optimal steffensen-type family for solving nonlinear equations.

Applied Mathematics and Computation, 217(23):9592–9597, 2011.

J. Li, X. Wang, and K. Madhu. Higher-order derivative-free iterative methods for solving nonlinear

equations and their basins of attraction. Mathematics, 7:11, 2019.

S. Li. Fourth-order iterative method without calculating the higher derivatives for nonlinear equation.

Journal of Algorithms Computational Technology, 13, 2019.

U. K Qureshi, Z. A. Kalhoro, A. A. Shaikh, and S. Jamali. Sixth Order Numerical Iterated Method of

Open Methods for Solving Nonlinear Applications Problems. Proceedings of the Pakistan Academy of

Sciences: A. Physical and Computational Sciences, 57(November):35–40, 2020.

U. K. Qureshi, S. Jamali, Z. A. Kalhoro, and A. G. Shaikh. Modified Quadrature Iterated Methods of

Boole Rule and Weddle Rule for Solving non-Linear Equations. Journal of Mechanics of continua and

Mathematical sciences, 16(2):87–101, 2021. ISSN 0973-8975. doi:

https://doi.org/10.26782/jmcms.202

02.00008.

U. K. Qureshi, S. Jamali, Z. A. Kalhoro, and G. Jinrui. Deprived of Second Derivative Iterated Method for

Solving Nonlinear Equations. Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational

Sciences, 58(2):39–44, dec 2021. ISSN 2518-4253. doi: https://doi.org/10.53560/PPASA(58-2)605.

D. Jain. Families of newton-like methods with fourth-order convergence. International Journal of computer

mathematics, 90(5):1072–1082, 2013.

F. Soleymani. Efficient optimal eighth-order derivative-free methods for nonlinear equations. Japan

Journal of Industrial and Applied Mathematics, 30(2):287–306, 2013.

A. S. Alshomrani, R. Behl, and V. Kanwar. An optimal reconstruction of chebyshev–halley type methods

for nonlinear equations having multiple zeros. Journal of Computational and Applied Mathematics,

:651–662, 2019.

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Published

2022-12-31

How to Cite

Jamali, S., Kalhoro, Z. A., Shaikh, A. W., Saleem Chandio, M., & Dehraj, S. (2022). A Novel Two Point Optimal Derivative free Method for Numerical Solution of Nonlinear Algebraic, Transcendental Equations and Application Problems using Weight Function. VFAST Transactions on Mathematics, 10(2), 137–146. https://doi.org/10.21015/vtm.v10i2.1288