Special Issue Editorial “Solvability of Nonlinear Equations with Parameters: Branching, Regularization, Group Symmetry and Solutions Blow-Up”

Sidorov, N. V.

doi:10.3390/sym14020226

Cited by 2 publications

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“…It is to be noted that loaded differential and loaded integro-differential equations are directly relevant to the non-local problem for integro-differential equations; see [10,11] and the references therein. Nevertheless, the problem of analyzing loaded systems of differential equations with bifurcation parameters is still an open problem despite the significant progress in nonlinear analysis [12].…”

Section: Introductionmentioning

confidence: 99%

Branching Solutions of the Cauchy Problem for Nonlinear Loaded Differential Equations with Bifurcation Parameters

Sidorov

2022

Mathematics

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The Cauchy problem for a nonlinear system of differential equations with a Stieltjes integral (loads) of the desired solution is considered. The equation contains bifurcation parameters where the system has a trivial solution for any values. The necessary and sufficient conditions are derived for those parameter values (bifurcation points) in the neighborhood of which the Cauchy problem has a non-trivial real solution. The constructive method is proposed for the solution of real solutions in the neighborhood of those points. The method uses successive approximations and builds asymptotics of the solution. The theoretical results are illustrated by example. The Cauchy problem with loads and bifurcation parameters has not been studied before.

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Section: Introductionmentioning

confidence: 99%

Branching Solutions of the Cauchy Problem for Nonlinear Loaded Differential Equations with Bifurcation Parameters

Sidorov

2022

Mathematics

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Stability Analysis of Simple Root Seeker for Nonlinear Equation

Wang

2023

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In this paper, the stability of a class of Liu–Wang’s optimal eighth-order single-parameter iterative methods for solving simple roots of nonlinear equations was studied by applying them to arbitrary quadratic polynomials. Under the Riemann sphere and scaling theorem, the complex dynamic behavior of the iterative method was analyzed by fractals. We discuss the stability of all fixed points and the parameter spaces starting from the critical points with the Mathematica software. The dynamical planes of the elements with good and bad dynamical behavior are given, and the optimal parameter element with stable behavior was obtained. Finally, a numerical experiment and practical application were carried out to prove the conclusion.

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Special Issue Editorial “Solvability of Nonlinear Equations with Parameters: Branching, Regularization, Group Symmetry and Solutions Blow-Up”

Abstract: Nonlinear dynamical models with parameters are at the heart of natural science, and they serve as essential instrument to analyze and solve various appealing problems in engineering areas [...]

Cited by 2 publications

References 7 publications

Branching Solutions of the Cauchy Problem for Nonlinear Loaded Differential Equations with Bifurcation Parameters

Branching Solutions of the Cauchy Problem for Nonlinear Loaded Differential Equations with Bifurcation Parameters

Stability Analysis of Simple Root Seeker for Nonlinear Equation

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