A New Second Derivative Free Iterative Method of Fifth Order of Convergence and Its Applications

Ayunda Putri, Imran M

Abstract


The primary objective of this article is to derive a new free from second derivative iterative method for solving nonlinear equations. The proposed method is proven to have fifth order of convergence. Comparisons with other iterative methods represent the advantage of the modified method. Observation on applications of the method in problem of chemical equilibrium , binary azeotropic problem, volume from van der Waals equations and eccentric anomaly in Kepler's law exhibits that our method is applicable and preferable.

Keywords


nonlinear equations, iterative method, Halley's method

Full Text:

PDF

References


Noor, M.A. and Noor, K.I., 2007, Fifth-order iterative methods for solving nonlinear equations, Applied mathematics and computation, Volume : 188(1), pp.406-410.

Gutierrez, J.M., Hernández, M.A., 1997, A family of Chebyshev-Halley type methods in Banach spaces, Bulletin of the Australian Mathematical Society, Volume : 55(1), pp.113-130.

Ahmad, F., Hussain, S., Hussain, S., Rafiq, A., 2013, New Ninth Order J-Halley Method for Solving Nonlinear Equations, Applied Mathematics, Volume : 4(12), p.1709.

Yu, X. and Xu, X., 2012, A new family of Chebyshev-Halley like methods free from second derivative, Fixed Point Theory, Volume : 13(1), pp.319-325.

Kou, J. and Li, Y., 2007, The improvements of Chebyshev–Halley methods with fifth-order convergence, Applied Mathematics and Computation, Volume : 188(1), pp.143-147.

Barrada, M., Benkhouya, R., Lahmer, M., Chana, I., 2021, On the Global Convergence of a New Super Halley’s Family for Solving Nonlinear Equations, Engineering Letters , Volume : 29(4).

Noor, M.A., Khan, W.A., Hussain, A., 2007, A new modified Halley method without second derivatives for nonlinear equation, Applied mathematics and computation, Volume : 189(2), pp.1268-1273.

Kou, J., Li, Y., Wang, X., 2007. A family of fifth-order iterations composed of Newton and third-order methods, Applied mathematics and computation, Volume : 186(2), pp.1258-1262.

Esmaeili, H., Rostami, M., 2014, A modification of Chebyshev-Halley method free from second derivatives for nonlinear equations, Caspian Journal of Mathematical Sciences (CJMS) peer, Volume : 3(1), pp.123-130.

Wartono, M., Suryani, I., 2016, Chebyshev-halley’s method without second derivative of eight-order convergence, Global Journal of Pure and Applied Mathematics, Volume : 12(4), pp.2987-2997.

Syakir, A., Imran, M., Gamal, M. D. H., 2017, Combination of Newton-Halley-Chebyshev Iterative Methods Without Second Derivatives, International Journal of Theoretical and Applied Mathematics, Volume : 3(3), pp.106-109.

Naseem, A., Rehman, M. A., Qureshi, S., Ide, N.A.D., 2023, Graphical and Numerical Study of a Newly Developed Root-Finding Algorithm and Its Engineering Applications, IEEE Access, Volume : 11, pp.2375-2383.

Yu, X., Xu, X., 2012, A new family of Chebyshev-Halley like methods free from second derivative, Fixed Point Theory, Volume : 13(1), pp.319-325.

Valkenburg, M.E.V., 2001, Reference Data fo Engineers Radio, Electronics, Computer and Communications, 9th Edition, Newnes, Boston.

Balaji, G.V., Seader, J. D., 1995, Application of interval Newton's method to chemical engineering problems, Reliable Computing, Volume : 1(3), pp.215-223.

Shacham, M., 1989. An improved memory method for the solution of a nonlinear equation, Chemical Engineering Science, Volume : 44(7), pp.1495-1501.

Shacham, M., Kehat, E., 1972, An iteration method with memory for the solution of a non-linear equation, Chemical Engineering Science, Volume : 27(11), pp.2099-2101.

Henley, E.J., Rosen, E. M., 1969, Material and Energy Balance Computations, 1st Edition, Wiley, New York.

Gautschi, W., 2011, Numerical analysis, 2nd Edition, Birkhauser Basel, Boston.

Burden, A. M., Faires, J. D., Burden, R.L., 2015, Numerical Analysis, 10th Edition, Cengage Learning, Boston.

Silbey, R. J., Alberty, R.A, Bawendi, M. G., 2004, Physical Chemistry, 4th Edition, Wiley.




DOI: https://doi.org/10.25077/jmua.12.4.283-292.2023

Refbacks

  • There are currently no refbacks.


Copyright (c) 2024 Jurnal Matematika UNAND

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Lisensi Creative Commons
Ciptaan disebarluaskan di bawah Lisensi Creative Commons Atribusi-BerbagiSerupa 4.0 Internasional.