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An extended radius of convergence comparison between two sixth order methods under general continuity for solving equations

Yıl 2022, Cilt: 6 Sayı: 3, 310 - 317, 30.09.2022
https://doi.org/10.31197/atnaa.1056652

Öz

In this paper, we compare the radii of convergence of two sixth convergence order methods for solving the nonlinear equations. We present the local convergence analysis not given before, which is based on the first Fréchet derivative that only appears on the method. Numerical examples where the theoretical results are tested complete the paper.

Kaynakça

  • [1] I.K. Argyros, A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach spaces, J. Math. Anal. Appl. 298 (2004) 374-397.
  • [2] I.K. Argyros, Convergence and Applications of Newton-Type Iterations, Springer-Verlag, New York, 2008.
  • [3] I.K. Argyros, Computational Theory of Iterative Methods, Series: Studies in Computational Mathematics, 15, Editors: Chui C.K. and Wuytack L. Elsevier Publ. Company, New York (2007).
  • [4] I.K. Argyros, Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications, Mathematics 2021, 9(16), 1942; https://doi. org/10.3390/math9161942.
  • [5] I.K. Argyros, A.A. Magreñán, Iterative method and their dynamics with applications, CRC Press, New York, USA, 2017.
  • [6] I.K. Argyros, S. George, A.A. Magreñán, Local convergence for multi-point- parametric Chebyshev-Halley-type method of higher convergence order. J. Comput. Appl. Math. 282, 215-224 (2015).
  • [7] I.K. Argyros, A.A. Magreñán, A study on the local convergence and the dynamics of Chebyshev-Halley-type methods free from second derivative. Numer. Algorithms 71, 1-23, (2015).
  • [8] I.K. Argyros, S. George, On the complexity of extending the convergence region for Traub's method, Journal of Complexity 56, 101423.
  • [9] I.K. Argyros, S. George, Mathematical modeling for the solution of equations and systems of equations with applications, Volume-IV, Nova Publishes, NY, 2020.
  • [10] D.K.R. Babajee, M.Z. Dauhoo, M.T. Darvishi, A. Karami, A. Barati, Analysis of two Chebyshev-like third order methods free from second derivatives for solving systems of nonlinear equations, J. Comput. Appl. Math. 233 (2010) 2002-2012.
  • [11] M.T. Darvishi, AQ two step high order Newton like method for solving systems of nonlinear equations, Int. J. Pure Appl. Math., 57(2009), 543-555.
  • [12] M. Grau-Sáchez, A. Grau, M. Noguera, Ostrowski type methods for solving systems of nonlinear equations, Appl. Math. Comput. 218 (2011) 2377-2385.
  • [13] J.P. Jaiswal, Semilocal convergnece of an eighth-order method in Banach spaces and its computational efficiency, Nu- mer.Algorithms 71 (2016) 933-951.
  • [14] J.P. Jaiswal, Analysis of semilocal convergence in Banach spaces under relaxed condition and computational efficiency, Numer. Anal. Appl. 10 (2017) 129-139.
  • [15] S. Regmi, I.K. Argyros, Undergraduate Research at Cameron University on Iterative Procedures in Banach and Other Spaces, Nova Science Publisher, NY, 2019.
  • [16] W.C. Rheinboldt, An adaptive continuation process for solving systems of nonlinear equations, In: Mathematical models and numerical methods (A.N.Tikhonov et al. eds.) pub.3, (1977), 129-142 Banach Center, Warsaw Poland.
  • [17] J.F. Traub, Iterative Methods for the Solution of Equations. Prentice-Hall, Englewood Cliffs(1964).
  • [18] J.R. Sharma, H. Arora, Improved Newton-like methods for solving systems of nonlinear equations, SeMA, 74, 147- 163,(2017).
  • [19] J.R. Sharma, D. Kumar, A fast and efficient composite Newton-Chebyshev method for systems of nonlinear equations, J. Complexity, 49, (2018), 56-73.
  • [20] R. Sharma, J.R. Sharma, N. Kalra, A modified Newton-Ozban composition for solving nonlinear systems, International J. of computational methods, 17, 8, (2020), world scientific publ. Comp.
  • [21] X. Wang, Y. Li, An efficient sixth order Newton type method for solving nonlinear systems, Algorithms, 10, 45, (2017), 1-9.
  • [22] S. Weerakoon, T.G.I. Fernando, A variant of Newton's method with accelerated third-orde rconvergence. Appl. Math. Lett.13, 87-93 (2000).
Yıl 2022, Cilt: 6 Sayı: 3, 310 - 317, 30.09.2022
https://doi.org/10.31197/atnaa.1056652

Öz

Kaynakça

  • [1] I.K. Argyros, A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach spaces, J. Math. Anal. Appl. 298 (2004) 374-397.
  • [2] I.K. Argyros, Convergence and Applications of Newton-Type Iterations, Springer-Verlag, New York, 2008.
  • [3] I.K. Argyros, Computational Theory of Iterative Methods, Series: Studies in Computational Mathematics, 15, Editors: Chui C.K. and Wuytack L. Elsevier Publ. Company, New York (2007).
  • [4] I.K. Argyros, Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications, Mathematics 2021, 9(16), 1942; https://doi. org/10.3390/math9161942.
  • [5] I.K. Argyros, A.A. Magreñán, Iterative method and their dynamics with applications, CRC Press, New York, USA, 2017.
  • [6] I.K. Argyros, S. George, A.A. Magreñán, Local convergence for multi-point- parametric Chebyshev-Halley-type method of higher convergence order. J. Comput. Appl. Math. 282, 215-224 (2015).
  • [7] I.K. Argyros, A.A. Magreñán, A study on the local convergence and the dynamics of Chebyshev-Halley-type methods free from second derivative. Numer. Algorithms 71, 1-23, (2015).
  • [8] I.K. Argyros, S. George, On the complexity of extending the convergence region for Traub's method, Journal of Complexity 56, 101423.
  • [9] I.K. Argyros, S. George, Mathematical modeling for the solution of equations and systems of equations with applications, Volume-IV, Nova Publishes, NY, 2020.
  • [10] D.K.R. Babajee, M.Z. Dauhoo, M.T. Darvishi, A. Karami, A. Barati, Analysis of two Chebyshev-like third order methods free from second derivatives for solving systems of nonlinear equations, J. Comput. Appl. Math. 233 (2010) 2002-2012.
  • [11] M.T. Darvishi, AQ two step high order Newton like method for solving systems of nonlinear equations, Int. J. Pure Appl. Math., 57(2009), 543-555.
  • [12] M. Grau-Sáchez, A. Grau, M. Noguera, Ostrowski type methods for solving systems of nonlinear equations, Appl. Math. Comput. 218 (2011) 2377-2385.
  • [13] J.P. Jaiswal, Semilocal convergnece of an eighth-order method in Banach spaces and its computational efficiency, Nu- mer.Algorithms 71 (2016) 933-951.
  • [14] J.P. Jaiswal, Analysis of semilocal convergence in Banach spaces under relaxed condition and computational efficiency, Numer. Anal. Appl. 10 (2017) 129-139.
  • [15] S. Regmi, I.K. Argyros, Undergraduate Research at Cameron University on Iterative Procedures in Banach and Other Spaces, Nova Science Publisher, NY, 2019.
  • [16] W.C. Rheinboldt, An adaptive continuation process for solving systems of nonlinear equations, In: Mathematical models and numerical methods (A.N.Tikhonov et al. eds.) pub.3, (1977), 129-142 Banach Center, Warsaw Poland.
  • [17] J.F. Traub, Iterative Methods for the Solution of Equations. Prentice-Hall, Englewood Cliffs(1964).
  • [18] J.R. Sharma, H. Arora, Improved Newton-like methods for solving systems of nonlinear equations, SeMA, 74, 147- 163,(2017).
  • [19] J.R. Sharma, D. Kumar, A fast and efficient composite Newton-Chebyshev method for systems of nonlinear equations, J. Complexity, 49, (2018), 56-73.
  • [20] R. Sharma, J.R. Sharma, N. Kalra, A modified Newton-Ozban composition for solving nonlinear systems, International J. of computational methods, 17, 8, (2020), world scientific publ. Comp.
  • [21] X. Wang, Y. Li, An efficient sixth order Newton type method for solving nonlinear systems, Algorithms, 10, 45, (2017), 1-9.
  • [22] S. Weerakoon, T.G.I. Fernando, A variant of Newton's method with accelerated third-orde rconvergence. Appl. Math. Lett.13, 87-93 (2000).
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Samundra Regmi 0000-0003-0035-1022

Ioannis K. Argyros 0000-0002-9189-9298

Santhosh George 0000-0002-3530-5539

Christopher Argyros Bu kişi benim

Yayımlanma Tarihi 30 Eylül 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 6 Sayı: 3

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