The objective of the current work is to invent and introduce the continuous version of Newton’s method. This scheme is used to establish some interesting properties with examples. We have plotted the fractal pattern graphs for a Newton-like met...
In this paper, we design a new third order Newton-like method and establish its convergence theory for finding the approximate solutions of nonlinear operator equations in the setting of Banach spaces. First, we discuss the convergence analysis of ou...
Recently, the high-order Newton-like methods have gained popularity for solving power flow problems due to their simplicity, versatility and, in some cases, efficiency. In this context, recent research studied the applicability of the 4th order Jarra...
In this study, we present a convergence analysis of a Newton-like midpoint method for solving nonlinear equations in a Banach space setting. The semilocal convergence is analyzed in two different ways. The first one is shown by replacing the existing...
We study the local convergence of an eighth order Newton-like method to approximate a locally-unique solution of a nonlinear equation. Earlier studies, such as Chen et al. (2015) show convergence under hypotheses on the seventh derivative or even hig...
Comparisons between Newton’s and Steffensen-like methods are given for solving systems of equations as well as Banach space valued equations. Our idea of the restricted convergence domain is used to compare the sufficient convergence criteria o...
In this work, we have developed a fourth order Newton-like method based on harmonic mean and its multi-step version for solving system of nonlinear equations. The new fourth order method requires evaluation of one function and two first order Fréchet...
The present paper includes the local and semilocal convergence analysis of a fourth-order method based on the quadrature formula in Banach spaces. The weaker hypotheses used are based only on the first Fréchet derivative. The new approach provides th...
In recent studies, the competitiveness of the Newton-S-Iteration-Process (Newton-SIP) techniques to efficiently solve the Power Flow (PF) problems in both well and ill-conditioned systems has been highlighted, concluding that these methods may be sui...
A three-step iterative method with fifth-order convergence as a new modification of Newton’s method was presented. This method is for finding multiple roots of nonlinear equation with unknown multiplicity m whose multiplicity m is the highest multipl...
We present a local convergence analysis of an eighth order three step methodin order to approximate a locally unique solution of nonlinear equation in a Banach spacesetting. In an earlier study by Sharma and Arora (2015), the order of convergence was...
The local convergence analysis of the
In this paper, we have obtained three optimal order Newton’s like methods of order four, eight, and sixteen for solving nonlinear algebraic equations. The convergence analysis of all the optimal order methods is discussed separately. We have discusse...
In the present paper, we introduced a quadratically convergent Newton-like normal S-iteration method free from the second derivative for the solution of nonlinear equations permitting
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...
In this paper, an iterative method for solving large, sparse systems of weakly nonlinear equations is presented. This method is based on Hermitian/skew-Hermitian splitting (HSS) scheme. Under suitable assumptions, we establish the convergence theorem...
The paper addresses an inverse problem for a nonlinear Volterra integral equation of the first kind with a piecewise continuous kernel whose discontinuity curves are the unknown functions. Such models arise in the theory of developing systems, power...
In this paper, we consider a fully discrete interpolated coefficient mixed finite element method for semilinear time fractional reaction–diffusion equations. The classic
A plethora of higher order iterative methods, involving derivatives in algorithms, are available in the literature for finding multiple roots. Contrary to this fact, the higher order methods without derivatives in the iteration are difficult to const...
A new gradient-like methodology has been developed for aeroengine diagnosis, determining the engine health condition, which is defined by the engine degradation from an undegraded state and uses measurements at various sensors distributed along the e...
We propose a novel family of seventh-order iterative methods for computing multiple zeros of a nonlinear function. The algorithm consists of three steps, of which the first two are the steps of recently developed Liu–Zhou fourth-order method, w...
For coded distributed computing (CDC), polynomial code is one prevalent encoding method for CDC (called Poly-CDC). It suffers from poor numerical stability due to the Vandermonde matrix serving as the coefficient matrix which needs to be inverted, an...
In the present paper, a fifth-order direct multistep block method is proposed for solving the second-order Delay Differential Equations (DDEs) directly with boundary conditions using constant step size. In many life sciences applications, a delay pla...
Understanding and modeling the effect of magnetic fields on flows that present separation properties, such as those over a backward-facing step (BFS), is critical due to its role in metallurgical processes, nuclear reactor cooling, plasma confinement...
Boundary reflections are usually treated as interference in underwater acoustic localization, yet their position-dependent delays can form a virtual aperture for a single transceiver. This paper develops a geometry-constrained method for exploiting t...
This work presents a comprehensive analysis of two cubic techniques for Power Flow (PF) studies. In this regard, the families of Weerakoon-like and Darvishi-like techniques are considered. Several theoretical findings are presented and posteriorly co...
In this work, we construct a family of seventh order iterative methods for finding multiple roots of a nonlinear function. The scheme consists of three steps, of which the first is Newton’s step and last two are the weighted-Newton steps. Hence...
The aim of this paper is to study, from a topological and geometrical point of view, the iteration map obtained by the application of iterative methods (Newton or relaxed Newton’s method) to a polynomial equation. In fact, we present a collection of...
While first-order methods are popular for solving optimization problems arising in deep learning, they come with some acute deficiencies. To overcome these shortcomings, there has been recent interest in introducing second-order information through q...
In this paper, we present a comparative study between Sinc–Galerkin method and a modified version of the variational iteration method (VIM) to solve non-linear Sturm–Liouville eigenvalue problem. In the Sinc method, the problem under cons...
In this paper, we analyze the Schwarzschild-like wormhole in the Asymptotically Safe Gravity(ASG) scenario. The ASG corrections are implemented via renormalization group methods, which, as consequence, provides a new tensor
Technical losses in transmission systems are crucial for short-term planning and decision-making, particularly in complex systems. Traditional deterministic methods like Newton–Raphson prove ineffective in handling systems with a large number o...
In this paper, we consider a generalized inexact Newton-Landweber iteration to solve nonlinear ill-posed inverse problems in Banach spaces, where the forward operator might not be Gâteaux differentiable. The method is designed with non-smooth c...
In this paper, we deal with some applications of the network simulation method (NMS) to the non-linear differential equations derived of a parametric family associated to stated problems by Newton in and others like the parabolic mirror and van der P...
We develop a new Kantorovich-like convergence analysis of Newton-type methods to solve nonsingular and singular nonlinear equations in Banach spaces. The outer or generalized inverses are exchanged by a finite sum of linear operators making the imple...
Finding arbitrary roots of polynomials is a fundamental problem in various areas of science and engineering. A myriad of methods was suggested to address this problem, such as the sequential Newton’s method and the Durand–Kerner (D–K) simultaneous it...
The most cited evidence for (non-baryonic) dark matter has been an apparent lack of visible mass to gravitationally support the observed orbital velocity of matter in rotating disk galaxies, yet measurement of the mass of celestial objects cannot be...
An adaptive Nesterov quasi-Newton acceleration (an-QNA)-optimized low-noise amplifier (LNA) is proposed in this paper. An optimized single-ended-to-differential two-stage LNA circuit is presented. It includes an improved post-linearization (IPL) tech...
In our paper, we present a sparse quasi-Newton method, called the sparse direct Broyden method, for solving sparse nonlinear equations. The method can be seen as a Broyden-like method and is a least change update satisfying the sparsity condition and...
In this paper, an on chip two-dimensional Newton’s ring-like plasmonic sensor is designed for differentiating the chirality of circularly polarized lights (CPLS). The structure of the plasmonic sensor consists of a circular arc slit and an arra...
The movement of isotropic and anisotropic particles of iron and graphite within the polymer matrix was predicted and examined by the COMSOL simulation method. The interfacial adhesion of filler particles within the matrix was investigated under surfa...
A parameter-free optimization technique is applied in Quasi-Newton’s method for solving unconstrained multiobjective optimization problems. The components of the Hessian matrix are constructed using q-derivative, which is positive definite at e...
In this paper, we focus on the design and analysis of a bionic gliding robotic dolphin. Inspired by natural dolphins, a novel bionic gliding robotic dolphin is developed. Different from the existing ones, the gliding robotic dolphin developed in this...
A critical reduction in the total harmonic distortion in the output voltage of multilevel inverters can be obtained with an appropriate selection of the angles to switch the power semiconductors at low frequency. Among the methods used to obtain the...
With the development of mature Computational Fluid Dynamics (CFD) tools for fluids (air and liquid) and Finite Element Methods (FEM) for solids and structures, many approaches have been proposed to tackle the so-called Fluid–Structure Interaction or...
In this paper, the parameter estimation problem of a truncated normal distribution is discussed based on the generalized progressive hybrid censored data. The desired maximum likelihood estimates of unknown quantities are firstly derived through the...
This paper explores the modeling and simulation of an innovative double-damper suspension system, evaluating its effectiveness through different test scenarios. The double damper integrates two individual dampers into a unified assembly. The modeling...
With the increasing proportion of grid-connected capacity of new energy units, such as wind power and photovoltaics, accurately constructing simulation models of these units is of great significance to the study of new power systems. However, the act...
The diamond-like carbon (DLC) coatings containing 1.6%, 5.3% and 9.4 at.% of Ti deposited by the radio frequency plasma enhanced chemical vapor deposition (RF PECVD) method on the silicon substrate were modified by n-decylphosphonic acid (DP) and 1H,...
The simulation of complex engineering structures built from magneto-rheological elastomers is a computationally challenging task. Using the FE
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