Fourth- and Fifth-Order Methods for Solving Nonlinear Systems of Equations: An Application to the Global Positioning System by Manuel F. Abad, Alicia Cordero, Juan R. Torregrosa

“…Two iterative methods of order four and five, respectively, are presented for solving nonlinear systems of equations. …”
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Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion by Jun Wang, Li-xin Lu, Huan-xin Jiang, Yong Zhu

“…An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.…”
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New Perturbation Iteration Solutions for Fredholm and Volterra Integral Equations by İhsan Timuçin Dolapçı, Mehmet Şenol, Mehmet Pakdemirli

“…In this paper, recently developed perturbation iteration method is used to solve Fredholm and Volterra integral equations. …”
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Block Preconditioned SSOR Methods for -Matrices Linear Systems by Zhao-Nian Pu, Xue-Zhong Wang

“…We present a block preconditioner and consider block preconditioned SSOR iterative methods for solving linear system . When is an -matrix, the convergence and some comparison results of the spectral radius for our methods are given. …”
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Convergence of Viscosity Iteration Process for a Finite Family of Generalized Asymptotically Quasi-Nonexpansive Mappings by Zhiming Cheng

“…We introduce a general iteration method for a finite family of generalized asymptotically quasi-nonexpansive mappings. …”
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Monte Carlo Alpha Iteration Algorithm for a Subcritical System Analysis by Hyung Jin Shim, Sang Hoon Jang, Soo Min Kang

“…The α-k iteration method which searches the fundamental mode alpha-eigenvalue via iterative updates of the fission source distribution has been successfully used for the Monte Carlo (MC) alpha-static calculations of supercritical systems. …”
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A New Biparametric Family of Two-Point Optimal Fourth-Order Multiple-Root Finders by Young Ik Kim, Young Hee Geum

“…We construct a biparametric family of fourth-order iterative methods to compute multiple roots of nonlinear equations. …”
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Periodic and Antiperiodic Solutions for a Second-Order Hamiltonian System With Nonlinearity Depending on Derivative by Wenxiong Chen, Shibo Liu

“…We prove that there exists T0>0 such that, for any T<T0, the provided Hamiltonian system has a nontrivial T-periodic and T/2-antiperiodic solution via linking theorem and iteration method.…”
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Some Matrix Iterations for Computing Matrix Sign Function by F. Soleymani, E. Tohidi, S. Shateyi, F. Khaksar Haghani

“…Some iterative methods are introduced and demonstrated for finding the matrix sign function. …”
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Descent methods for convex optimization problems in Banach spaces by M. S. S. Ali

“…We propose a general class of iterative methods, which are based on combining descent and regularization approaches and provide strong convergence of iteration sequences to a solution of the initial problem.…”
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The Iteration Solution of Matrix Equation AXB=C Subject to a Linear Matrix Inequality Constraint by Na Huang, Changfeng Ma

“…We propose a feasible and effective iteration method to find solutions to the matrix equation AXB=C subject to a matrix inequality constraint DXE≥F, where DXE≥F means that the matrix DXE-F is nonnegative. …”
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On the Existence and Uniqueness Results for Fuzzy Linear and Semilinear Fractional Evolution Equations Involving Caputo Fractional Derivative by Ali El Mfadel, Said Melliani, M’hamed Elomari

“…The existence theorems are proved by using fuzzy fractional calculus, Picard’s iteration method, and Banach contraction principle. As application, we conclude this paper by giving an illustrative example to demonstrate the applicability of the obtained results.…”
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Strong Convergence Analysis of Iterative Algorithms for Solving Variational Inclusions and Fixed-Point Problems of Pseudocontractive Operators by Zhangsong Yao, Yan-Kuen Wu, Ching-Feng Wen

“…Iterative methods for solving variational inclusions and fixed-point problems have been considered and investigated by many scholars. …”
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On the numerical solving of one minimization problem by Raimondas Čiegis, Violeta Pakenienė

“… In this paper we consider the dependence of iterative methods convergence rate on iterative parameters selection. …”
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Decomposition Technique and a Family of Efficient Schemes for Nonlinear Equations by Farooq Ahmed Shah, Maslina Darus, Imran Faisal, Muhammad Arsalan Shafiq

“…In this paper, a new family of iterative methods for solving nonlinear equations is developed by using a new decomposition technique. …”
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A General Class of Derivative Free Optimal Root Finding Methods Based on Rational Interpolation by Fiza Zafar, Nusrat Yasmin, Saima Akram, Moin-ud-Din Junjua

“…We construct a new general class of derivative free n-point iterative methods of optimal order of convergence 2n-1 using rational interpolant. …”
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Multigrid Discretization and Iterative Algorithm for Mixed Variational Formulation of the Eigenvalue Problem of Electric Field by Yidu Yang, Yu Zhang, Hai Bi

“…Combining the mixed finite element method with the Rayleigh quotient iteration method, a new multi-grid discretization scheme and an adaptive algorithm are proposed and applied to the eigenvalue problem of electric field. …”
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First-Order Boundary Value Problem with Nonlinear Boundary Condition on Time Scales by Ya-Hong Zhao

“…By applying monotone iteration method, we not only obtain the existence of positive solutions, but also establish iterative schemes for approximating the solutions.…”
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An Extension of the Optimal Homotopy Asymptotic Method to Coupled Schrödinger-KdV Equation by Hakeem Ullah, Saeed Islam, Muhammad Idrees, Mehreen Fiza, Zahoor Ul Haq

“…We obtained the extended OHAM solution of the problem and compared with the exact, variational iteration method (VIM) and homotopy perturbation method (HPM) solutions. …”
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Solutions of Conformable Fractional-Order SIR Epidemic Model by Atimad Harir, Said Malliani, Lalla Saadia Chandli

“…In this paper, the conformable fractional-order SIR epidemic model are solved by means of an analytic technique for nonlinear problems, namely, the conformable fractional differential transformation method (CFDTM) and variational iteration method (VIM). These models are nonlinear system of conformable fractional differential equation (CFDE) that has no analytic solution. …”
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