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2023 | OriginalPaper | Chapter

A Computationally Efficient Sixth-Order Method for Nonlinear Models

Authors : Janak Raj Sharma, Harmandeep Singh

Published in: Frontiers in Industrial and Applied Mathematics

Publisher: Springer Nature Singapore

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Abstract

The chapter introduces a computationally efficient sixth-order method for solving nonlinear models, addressing the challenge of obtaining analytical solutions for nonlinear systems. It builds on iterative methods, particularly Newton's method, and presents a three-step iterative scheme that maximizes convergence order without additional inverse operator evaluations. The method is thoroughly analyzed for computational efficiency and compared with existing sixth-order methods. Numerical experimentation on various nonlinear problems demonstrates the superior performance and stability of the proposed method, validating its theoretical convergence order and computational advantages.

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Avazzadeh, Z., Heydari, M., Loghmani, G.B.: Numerical solution of Fredholm integral equations of the second kind by using integral mean value theorem. Appl. Math. Model. 35, 2374–2383 (2011). https://doi.org/10.1016/j.apm.2010.11.056CrossRefMATH

Bahl, A., Cordero, A., Sharma, R., Torregrosa, J.R.: A novel bi-parametric sixth order iterative scheme for solving nonlinear systems and its dynamics. Appl. Math. Comput. 357, 147–166 (2019). https://doi.org/10.1016/j.amc.2019.04.003CrossRefMATH

Cordero, A., Hueso, J.L., Martínez, E., Torregrosa, J.R.: Efficient high-order methods based on golden ratio for nonlinear systems. Appl. Math. Comput. 217, 4548–4556 (2011). https://doi.org/10.1016/j.amc.2010.11.006CrossRefMATH

Cordero, A., Hueso, J.L., Martínez, E., Torregrosa, J.R.: Increasing the convergence order of an iterative method for nonlinear systems. Appl. Math. Lett. 25, 2369–2374 (2012). https://doi.org/10.1016/j.aml.2012.07.005CrossRefMATH

Esmaeili, H., Ahmadi, M.: An efficient three-step method to solve system of nonlinear equations. Appl. Math. Comput. 266, 1093–1101 (2015). https://doi.org/10.1016/j.amc.2015.05.076CrossRefMATH

Lotfi, T., Bakhtiari, P., Cordero, A., Mahdiani, K., Torregrosa, J.R.: Some new efficient multipoint iterative methods for solving nonlinear systems of equations. Int. J. Comput. Math. 92, 1921–1934 (2014). https://doi.org/10.1080/00207160.2014.946412CrossRefMATH

Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York (1970)MATH

Ostrowski, A.M.: Solution of Equation and Systems of Equations. Academic Press, New York (1960)MATH

Potra, F.A., Pták, V.: On a class of modified Newton processes. Numer. Funct. Anal. Optim. 2, 107–120 (1980). https://doi.org/10.1080/01630568008816049CrossRefMATH

10.

Sharma, J.R., Gupta, P.: An efficient fifth order method for solving systems of nonlinear equations. Comput. Math. Appl. 67, 591–601 (2014). https://doi.org/10.1016/j.camwa.2013.12.004CrossRefMATH

11.

Sharma, R., Sharma, J.R., Kalra, N.: A modified Newton-Özban composition for solving nonlinear systems. Int. J. Comput. Methods 17, 1950047 (2020). https://doi.org/10.1142/S0219876219500476CrossRefMATH

12.

Soleymani, F., Lotfi, T., Bakhtiari, P.: A multi-step class of iterative methods for nonlinear systems. Optim. Lett. 8, 1001–1015 (2014). https://doi.org/10.1007/s11590-013-0617-6CrossRefMATH

13.

Traub, J.F.: Iterative Methods for the Solution of Equations. Chelsea Publishing Company, New York (1982)MATH

14.

Wang, X., Kou, J., Gu, C.: Semilocal convergence of a sixth-order Jarratt method in Banach spaces. Numer. Algor. 57, 441–456 (2011). https://doi.org/10.1007/s11075-010-9438-1CrossRefMATH

15.

Wolfram, S.: The Mathematica Book. Wolfram Media, USA (2003)

Title: A Computationally Efficient Sixth-Order Method for Nonlinear Models
Authors: Janak Raj Sharma
Harmandeep Singh
Publisher: Springer Nature Singapore
Book: Frontiers in Industrial and Applied Mathematics
Print ISBN: 978-981-19-7271-3

Electronic ISBN: 978-981-19-7272-0

Copyright Year: 2023
DOI: https://doi.org/10.1007/978-981-19-7272-0_39

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