Related papers: Some Classes of third and Fourth-order iterative m…
This manuscript presents a novel and reliable third-order iterative procedure for computing the zeros of solutions to second-order ordinary differential equations. By approximating the solution of the related Riccati differential equation…
In the paper [Muhammad Aslam Noor, Khalida Inayat Noor, Three-step iterative methods for nonlinear equations, Applied Mathematics and Computation, 183 (2006), pp. 322-327 ], Authors presented an algorithm (\textbf{Algorithm 2.3}) and stated…
This paper demonstrates new methods and implementations of nonlinear solvers with higher-order of convergence, which is achieved by efficiently computing higher-order derivatives. Instead of computing full derivatives, which could be…
In this paper, we propose a class of super-schemes for efficiently solving nonlinear unconstrained optimization problems. The proposed approach introduces two novel choices of step-size parameters, leading to efficient descent directions…
This article generalizes a recently introduced procedure to solve nonlinear systems of equations, radically departing from the conventional Newton-Raphson scheme. The original nonlinear system is first unfolded into three simpler…
In this paper, we introduce the new optimal perturbation iteration method based on the perturbation iteration algorithms for the approximate solutions of nonlinear differential equations of many types. The proposed method is illustrated by…
In (Nucci M.C. 1994, Physica D 78 p.124), we have found that iterations of the nonclassical symmetries method give rise to new nonlinear equations, which inherit the Lie point symmetry algebra of the given equation. In the present paper, we…
We describe a set of Gaussian Process based approaches that can be used to solve non-linear Ordinary Differential Equations. We suggest an explicit probabilistic solver and two implicit methods, one analogous to Picard iteration and the…
This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting…
A wide variety of (fixed-point) iterative methods for the solution of nonlinear equations (in Hilbert spaces) exists. In many cases, such schemes can be interpreted as iterative local linearization methods, which, as will be shown, can be…
This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting…
We describe a three precision variant of Newton's method for nonlinear equations. We evaluate the nonlinear residual in double precision, store the Jacobian matrix in single precision, and solve the equation for the Newton step with…
We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…
Four new variants of the Computational Order of Convergence (COC) of a one-point iterative method with memory for solving nonlinear equations are presented. Furthermore, the way to approximate the new variants to the local order of…
We present the results of the computation of a twisting type N solution to vacuum Einstein equations following an iterative approach. Our results show that the higher order terms fail to provide a full exact solution with non-vanishing…
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…
A new analytic approximate technique for addressing nonlinear problems, namely the optimal perturbation iteration method, is introduced and implemented to singular initial value Lane-Emden type problems to test the effectiveness and…
We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on q-order Taylor models (with q >= 1) that have been recently…
We present two algorithms for computing what we call the absolute factorization of a difference operator. We also give an algorithm to solve third order difference equations in terms of second order equations, together with applications to…
We establish or refute the optimality of inexact second-order methods for unconstrained nonconvex optimization from the point of view of worst-case evaluation complexity, improving and generalizing the results of Cartis, Gould and Toint…