96
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Generalized multistep Steffensen iterative method. Solving the model of a photomultiplier device

, &
Pages 1839-1859 | Received 24 Jan 2022, Accepted 18 May 2023, Published online: 02 Jun 2023

References

  • V. Alarcón, S. Amat, S. Busquier, and D.J. López, Steffensen's type method in Banach spaces with applications on boundary-value problems, J. Comput. Appl. Math. 216 (2008), pp. 243–250.
  • S. Amat, S. Busquier, A. Grau, and M. Grau-Sánchez, Maximum efficiency for a family of Newton-like methods with frozen derivatives and some applications, Appl. Math. Comput. 219 (2013), pp. 7954–7963.
  • S. Amat, J.A. Ezquerro, and M.A. Hernández, On a Steffensen-like method for solving nonlinear equations, Calcolo 53 (2016), pp. 171–188.
  • I.K. Argyros, A new convergence theorem for Steffensen's method on Banach spaces and applications, Southwest J. Pure Appl. Math. 1 (1997), pp. 23–29.
  • D.D. Bruns and J.E. Bailey, Nonlinear feedback control for operating a nonisothermal CSTR near an unstable steady state, Chem. Eng. Sci. 32 (1977), pp. 257–264.
  • A. Cordero, J.L. Hueso, E. Martínez, and J.R. Torregrosa, A modified Newton-Jarratt's composition, Numer. Algorithms 55 (2010), pp. 87–99.
  • A. Cordero and J.R. Torregrosa, Variants of Newton's method using fifth-order quadrature formulas, Appl. Math. Comput. 190 (2007), pp. 686–698.
  • J.A. Ezquerro, M.A. Hernández, N. Romero, and A.I. Velasco, On Steffensen's method on Banach spaces, J. Comput. Appl. Math. 249 (2013), pp. 9–23.
  •   Hamamatsu, Photomultiplier Tubes, Basics and Applications, 4th ed., Available at https://www.hamamatsu.com/resources/pdf/etd/PMT_handbook_v4E.pdf, retrieved in january 2022.
  • M.A. Hernández-Verón, Eulalia Martánez, and C. Teruel, Semilocal convergence of a k-step iterative process and its application for solving a special kind of conservative problems, Numer. Algor.76 (2017), pp. 309–331.
  • C.L. Howk, J.L. Hueso, Eulalia Martínez, and C. Teruel, A class of efficient high-order iterative methods with memory for nonlinear equations and their dynamics, Math. Methods Appl. Sci. 41 (2018), pp. 7263–7282.
  • F. Hueso-González, D. Ginestar, J.L. Hueso, and J. Riera, Comments on ‘SPICE model of photomultiplier tube under different bias conditions’, IEEE Sens. J. 21 (2021), pp. 17395–17402.
  • H.T. Kung and J.F. Traub, Optimal order of one-point and multi-point iteration, J. ACM 21 (1974), pp. 643–651.
  • M. Narang, S. Bhatia, A.Saleh Alshomrani, and V. Kanwar, General efficient class of Steffensen type methods with memory for solving systems of nonlinear equations, J. Comput. Appl. Math. 352 (2019), pp. 23–39.
  • J.M. Ortega, The Newton-Kantorovich theorem, Amer. Math. Monthly 75 (1968), pp. 658–660.
  • J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
  • A.M. Ostrowski, Solutions of Equations and System of Equations, Academic Press, New York, 1960.
  • J.F. Traub, Iterative Methods for the Solution of Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1964.
  • A.M. Wazwaz, Applications of Integral Equations, Linear and Nonlinear Integral Equations, Springer, Berlin/Heidelberg, Germany, 2011.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.