4,068 Results Found

In this paper, we introduce a new family of efficient and optimal iterative methods for finding multiple roots of nonlinear equations with known multiplicity $(m\ge 1)$ . We use the weight function approach involving one and two parameters t...

The vibrations of the dynamical system play an important role in biological processes, electrical engineering, and mechanical structures. In this work, we focus on the behaviors of dynamical systems, such as periodical or damped oscillations and asym...

A nonlinear equation $f\left(x\right)=0$ is mathematically transformed to a coupled system of quasi-linear equations in the two-dimensional space. Then, a linearized approximation renders a fractional iterative scheme $x_{n+1}=x_n-f\left(x_n\right)/[a+bf\left(x_n\right)]$, which require...

In this paper, an efficient iterative method based on the generalized multiscale finite element (Iter-GMs) method is applied to solve the distributed optimal control problems governed by stochastic parabolic equations. Within this framework, we first...

Numerous applications from electrical engineering and mechanical structures are mathematically modeled using dynamical systems theory. Our paper concerns the behaviors of a 3D dynamic system in terms of damped or periodical oscillations and asymptoti...

In many fields of science and engineering, partial differential equation (PDE) constrained optimal control problems are widely used. We mainly solve the optimization problem constrained by the time-periodic eddy current equation in this paper. We pro...

This paper proposes an Enhanced Projection-Iterative-Methods-based Optimizer (EPIMO) to overcome the limitations of its predecessor, the Projection-Iterative-Methods-based Optimizer (PIMO), including deterministic parameter decay, insufficient divers...

Class function/shape function transformation (CST) is an advanced geometry representation method employed to generate airfoil coordinates. Aiming at the morbidity of the CST coefficient matrix, the pivot element weighting iterative (PEWI) method is p...

This paper proposes a new proximal iteratively reweighted nuclear norm method for a class of nonconvex and nonsmooth optimization problems. The primary contribution of this work is the incorporation of line search technique based on dimensionality re...

This paper investigates the damped and periodical oscillations of a specific system that depends on four physical parameters. Exact parametric solutions are established based on a smooth function. The system is explicitly integrated without admitting...

In this paper, we construct variants of Bawazir’s iterative methods for solving nonlinear equations having simple roots. The proposed methods are two-step and three-step methods, with and without memory. The Newton method, weight function and d...

In this study, we improve the matching accuracy of underwater gravity matching navigation. Firstly, the Iterative Optimal Annulus Point (IOAP) method with a novel grid topology is proposed for breaking through the inherent grid structure limit of the...

In the paper, two nonlinear variants of the Newton method are developed for solving nonlinear equations. The derivative-free nonlinear fractional type of the one-step iterative scheme of a fourth-order convergence contains three parameters, whose opt...

Bearings are core components in many types of industrial equipment, and their operating environment is often accompanied by strong background noise. This results in a low Signal-to-Noise Ratio (SNR) in the collected vibration signals, making it diffi...

We derive a double-optimal iterative algorithm (DOIA) in an m-degree matrix pencil Krylov subspace to solve a rectangular linear matrix equation. Expressing the iterative solution in a matrix pencil and using two optimization techniques, we determine...

Intelligent reflecting surfaces (IRSs) have been recognized as a disruptive and revolutionary technology for achieving efficient and secure information transmission. This paper investigates beamforming optimization methods for an IRS-aided MIMO syste...

In this paper, some one-step iterative schemes with memory-accelerating methods are proposed to update three critical values $f^{\prime }\left(r\right)$, $f^{″}\left(r\right)$, and $f^{‴}\left(r\right)$ of a nonlinear equation $f\left(x\right)=0$ with r being its simple root. We can achieve high va...

A Steam generator is a crucial device of a nuclear power plant. Control performance of the steam generator level control system is key to its normal operation. To improve its performance, the control system parameters should be optimized by utilizing...

The newly constructed optimal perturbation iteration procedure with Laplace transform is applied to obtain the new approximate semi-analytical solutions of the fractional type of damped Burgers’ equation. The classical damped Burgers’ equ...

Many optimal order multiple root techniques involving derivatives have been proposed in literature. On the contrary, optimal order multiple root techniques without derivatives are almost nonexistent. With this as a motivational factor, here we develo...

There is no doubt that the fourth-order King’s family is one of the important ones among its counterparts. However, it has two major problems: the first one is the calculation of the first-order derivative; secondly, it has a linear order of converge...

In this paper, we study the improved block splitting (IBS) iteration method and its accelerated variant, the accelerated improved block splitting (AIBS) iteration method, for solving linear systems of equations stemming from the discretization of the...

For further insight into the perturbation technique within the framework of the asymptotic iteration method (PAIM), we suggest this method to be used as an alternative method to the traditional well-known perturbation techniques. We show by means of...

This study focuses on improving the application of the quadratic penalty smoothing technique for solving the fuel-optimal problem of low-thrust trajectory. Some practical techniques, including the Particle Swarm Optimization algorithm (PSO), the co-s...

The Shimizu–Morioka dynamical system is analytically investigated in this paper by means of the Optimal Auxiliary Functions Method (OAFM). This system has a chaotic dynamical behavior, specified for more physical applications as chaos synchroni...

In this manuscript, we propose a parametric family of iterative methods of fourth-order convergence, and the stability of the class is studied through the use of tools of complex dynamics. We obtain the fixed and critical points of the rational opera...

The goal of this paper is to build some approximate closed-form solutions for a class of dynamical systems involving a Hamilton–Poisson part. The chaotic behaviors are neglected. These solutions are obtained by means of a new version of the opt...

This study introduces a novel, iterative algorithm that achieves fourth-order convergence for solving nonlinear equations. Satisfying the Kung–Traub conjecture, the proposed technique achieves an optimal order of four with an efficiency index $($...

Many problems in science, engineering, and economics require solving of nonlinear equations, often arising from attempts to model natural systems and predict their behavior. In this context, iterative methods provide an effective approach to approxim...

The development of electric quarry transport puts a significant strain on local power grids, leading to sharp peaks in consumption and degradation of power quality. Existing methods of peak smoothing, such as generation control, virtual power plants,...

Several problems have been solved by nonlinear equation systems (NESs), including real-life issues in chemistry and neurophysiology. However, the accuracy of solutions is highly dependent on the efficiency of the algorithm used. In this paper, a Modi...

This work proposes a new simplified five-parameter estimation method for a single-diode model of photovoltaic panels. The method, based on an iterative algorithm, is able to estimate the parameter of the electrical single-diode model from the panel&r...

In a competitive electricity market, generation capacities can exactly cover their full costs. However, the real market deviates from this ideal in some aspects. One is the concern of non-existent or insufficient scarcity prices. We present an iterat...

Here, we propose optimal fourth-order iterative methods for approximating multiple zeros of univariate functions. The proposed family is composed of two stages and requires 3 functional values at each iteration. We also suggest an extensive convergen...

An improved optimizer based on projection-iterative methods (IPIMO) is proposed to address the optimal configuration problem of multi-type energy storage systems (MT-ESS), with the objective of achieving synergistic minimization of comprehensive cost...

In this manuscript, we introduce a novel parametric family of multistep iterative methods designed to solve nonlinear equations. This family is derived from a damped Newton’s scheme but includes an additional Newton step with a weight function...

Mathematical models and numerical simulations are necessary to understand the dynamical behaviors of complex systems. The aim of this work is to investigate closed-form solutions for the ball–plate problem considering a system derived from an o...

Three new iterative methods for solving scalar nonlinear equations using weight function technique are presented. The first one is a two-step fifth order method with four function evaluations which is improved from a two-step Newton’s method ha...

In annealing, steel coils should be heated and consequently cooled according to the technological prescription defined for the annealed type of steel. It is appropriate to develop the systems and methods for estimation of the steel coil inner tempera...

The aim of this paper is to introduce new high order iterative methods for multiple roots of the nonlinear scalar equation; this is a demanding task in the area of computational mathematics and numerical analysis. Specifically, we present a new Cheby...

This article introduces two enhanced techniques: the Natural Transform Iterative Method (NTIM) and the Optimal Auxiliary Function Method (OAFM). These approaches provide a close approximation for solving fractional-order Navier–Stokes equations...

Electrical capacitance tomography (ECT) attempts to reconstruct the permittivity distribution of the cross-section of measurement objects from the capacitance measurement data, in which reconstruction algorithms play a crucial role in real applicatio...

This paper presents new optimal eighth-order families with weight functions for solving nonlinear systems, obtained as a generalization of the first optimal eighth-order CTT8 method introduced by Cordero, Torregrosa and Triguero-Navarro. The proposed...

The main aim of this work is to introduce an implicit general iterative method for approximating a solution of a split variational inclusion problem with a hierarchical optimization problem constraint for a countable family of mappings, which are non...

With access to new energy sources, the problem of reactive power optimization and dispatching has become increasingly important for research. However, the reactive power optimization problem is a mixed integer nonlinear optimization problem. In order...

In this study, we propose an extension of the modified Newton-Househölder methods to find multiple roots with unknown multiplicity of nonlinear equations. With four functional evaluations per iteration, the proposed method achieves an optimal eighth...

Determining a reasonable main cable curve is the foundation of suspension bridge design, and the accuracy and efficiency of the curve-finding problem are key to the design of a suspension bridge. To accurately obtain the completed curve of a main cab...

Finding a repeated zero for a nonlinear equation $f\left(x\right)=0$ , $f:I\subseteq R\to R$ has always been of much interest and attention due to its wide applications in many fields of science and engineering. Modified Newton’s metho...

In this paper, the inverse problem of identifying the source term of the time fractional diffusion-wave equation is studied. This problem is ill-posed, i.e., the solution (if it exists) does not depend on the measurable data. Under the priori bound c...

In this manuscript, we introduce the higher-order optimal derivative-free family of Chebyshev–Halley’s iterative technique to solve the nonlinear equation having the multiple roots. The designed scheme makes use of the weight function and one paramet...