Algorithmizing for solving nonlinear equations using the variational iteration technique
DOI:
https://doi.org/10.5377/farem.v11i41.13886Keywords:
Iteration, variational, convergence, comparisonAbstract
This work deals with the variational iteration technique which is an iterative method for solving nonlinear equations of the form f(x)=0. In this sense, the main objective is to generate new algorithms and iterative schemes that allow obtaining new formulas and iterative methods. New formulas are created by means of mathematical procedures based on variants of Newton’s method and variational iteration techniques. In addition, the constructive developments of the main iterative schemes are expressed. The main iterative schemes of each method are obtained by means of the deduction of their construction, as well as the convergence analysis by means of the computational application in the Python programming language. Roots of nonlinear equations of some basis functions, used in the scientific articles consulted, which have the characteristics of being continuous and differentiable, are exemplified and calculated. On the other hand, a comparison is made between some of the existing algorithms and those designed in this research, using the criteria of maximum and minimum number of functional evaluations. These aspects are fundamental for the validity of the new algorithms. According to the results obtained after the various comparisons, the algorithms present an excellent performance with respect to those existing in the literature on this area of knowledge.
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References
Cisneros, I. (2017). Algoritmos basados en los Polinomios de Adomian e Iteracin Variacional para la resolucin de ecuaciones no lineales. Managua: UNAN - Managua.
Diloné, M. (2013). Métodos iterativos aplicados a la ecuación de Kepler. España: Universidad de la Rioja.
Inokuti, M., Sekine, H., & Mura, T. (1978). General Use of the Lagrange Multiplier in Nonlinear Mathematical Physics. Nemat-Nasser, pp. 156-162.
King, R. (1973). A family of fourth-order methods for nonlinear equations. SIAM .
Melan, A. (1997). Geometry and Convergence of Euler´s and Halley´s Methods. . SIAM, 728-735.
Noor, K., & Noor, M. (2007). Iterative methods with fourth-order convergence for nonlinear equations. Appl. Math. Comput, 221-227.
Noor, M., Shah, F., Noor, K., & Al-Said, E. (2011). Variational iteration technique for finding multiple roots of nonlinear equations. Sci. Res. Essays, 1344–1350.
Noor, M., Waseem, M., Noor, K., & Al-Said, E. (2012). Variational iteration technique for solving a system of nonlinear equations. . Optim. Lett. DOI: 10. 1007/s11590-012-0479-3.
Severance, C. (2020). Python para todos. Explorando la información con Python 3. MI, USA: Ann Arbor.
Shah, F. (2012). Variational iteration technique and Numerical Methods for solving nonlinear equations.
Traub, J. (1964). Iterative Methods for the Solution of Equations. , , . New Jersey, USA.: Prentice-Hall Englewood Cliffs.
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