Journal of Mathematical Chemistry

, Volume 55, Issue 7, pp 1443–1460 | Cite as

A family of parametric schemes of arbitrary even order for solving nonlinear models: CMMSE2016

  • Alicia Cordero
  • Juan R. Torregrosa
  • María P. Vassileva
Original Paper
  • 137 Downloads

Abstract

Many problems related to gas dynamics, heat transfer or chemical reactions are modeled by means of partial differential equations that usually are solved by using approximation techniques. When they are transformed in nonlinear systems of equations via a discretization process, this system is big-sized and high-order iterative methods are specially useful. In this paper, we construct a new family of parametric iterative methods with arbitrary even order, based on the extension of Ostrowski’ and Chun’s methods for solving nonlinear systems. Some elements of the proposed class are known methods meanwhile others are new schemes with good properties. Some numerical tests confirm the theoretical results and allow us to compare the numerical results obtained by applying new methods and known ones on academical examples. In addition, we apply one of our methods for approximating the solution of a heat conduction problem described by a parabolic partial differential equation.

Keywords

System of nonlinear equations Iterative methods Order of convergence Heat conduction problem Divided differences 

Notes

Acknowledgements

This research was partially supported by Ministerio de Economía y Competitividad MTM2014-52016-C02-2-P and FONDOCYT 2014-1C1-088 República Dominicana.

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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Alicia Cordero
    • 1
  • Juan R. Torregrosa
    • 1
  • María P. Vassileva
    • 2
  1. 1.Instituto de Matemática Multidisciplinar, Universitat Politècnica de ValènciaValenciaSpain
  2. 2.Instituto Tecnológico de Santo Domingo (INTEC)Santo DomingoDominican Republic

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