Other algorithmic variants for solving nonlinear equations based on the variational iteration technique
DOI:
https://doi.org/10.5377/rtu.v12i34.16341Keywords:
Algorithms, Convergence, Iteratives, Methods, ComparisonAbstract
This paper addresses a continuity of new algorithmic versions on 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 new iterative formulas and methods to be obtained.
It also studies the constructive development and convergence of each of the methods presented under which the technique variational iteration appears as a fundamental axis for solving various types of nonlinear equations, therefore, new formulas are created using mathematical procedures based on Newton's method variants and variational iteration techniques.
The obtaining of the main iterative schemes of each method by deducting its construction, as well as the convergence analysis by means of the computational application were done in the Python programming language. In fact, the roots of non-linear equations of some basic functions, used in the scientific articles consulted, which have 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 to the validity of the new algorithmic variants for solving nonlinear equations based on the variational iteration technique.
According to the results obtained after the various comparisons, the algorithms have an excellent function with respect to those existing in the literature on this area of knowledge.
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