A Novel Two Point Optimal Derivative free Method for Numerical Solution of Nonlinear Algebraic, Transcendental Equations and Application Problems using Weight Function
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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.
DOI: http://dx.doi.org/10.21015/vtm.v10i2.1288
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