Design of High-Order Iterative Methods for Nonlinear Systems by Using Weight Function Procedure by Santiago Artidiello, Alicia Cordero, Juan R. Torregrosa, María P. Vassileva

“…We present two classes of iterative methods whose orders of convergence are four and five, respectively, for solving systems of nonlinear equations, by using the technique of weight functions in each step. …”
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General Iterative Methods for Equilibrium Problems and Infinitely Many Strict Pseudocontractions in Hilbert Spaces by Peichao Duan, Aihong Wang

“…We propose an implicit iterative scheme and an explicit iterative scheme for finding a common element of the set of fixed point of infinitely many strict pseudocontractive mappings and the set of solutions of an equilibrium problem by the general iterative methods. In the setting of real Hilbert spaces, strong convergence theorems are proved. …”
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Convergence of Variational Iteration Method for Solving Singular Partial Differential Equations of Fractional Order by Asma Ali Elbeleze, Adem Kılıçman, Bachok M. Taib

“…The variational iteration method (VIM) is applied to obtain approximate solutions of this type of equations. …”
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Fractional Variational Iteration Method for Solving Fractional Partial Differential Equations with Proportional Delay by Brajesh Kumar Singh, Pramod Kumar

“…This paper deals with an alternative approximate analytic solution to time fractional partial differential equations (TFPDEs) with proportional delay, obtained by using fractional variational iteration method, where the fractional derivative is taken in Caputo sense. …”
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Fatigue Analysis of a Light Truck Rear Axle Based on Virtual Iteration Method by Donglong Zhou, Jianlong Chang

“…Taking the road test signals as the iterative target and the vehicle MBD model as the iterative carrier, the vehicle equivalent excitation is obtained by using the VIM (virtual iteration method). By applying the equivalent excitation obtained by VIM to the vehicle MBD model, the load spectra of key points of the driving rear axle are obtained. …”
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Analysis of Nonlinear Vibration of Hard Coating Thin Plate by Finite Element Iteration Method by Hui Li, Liu Ying, Wei Sun

“…This paper studies nonlinear vibration mechanism of hard coating thin plate based on macroscopic vibration theory and proposes finite element iteration method (FEIM) to theoretically calculate its nature frequency and vibration response. …”
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Higher-Order Convergent Iterative Method for Computing the Generalized Inverse over Banach Spaces by Xiaoji Liu, Fu Huang

“…A higher-order convergent iterative method is provided for calculating the generalized inverse over Banach spaces. …”
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Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method by Asfaw Tsegaye Moltot, Alemayehu Tamirie Deresse

“…In this study, an efficient analytical method called the Sumudu Iterative Method (SIM) is introduced to obtain the solutions for the nonlinear delay differential equation (NDDE). …”
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A New Family of Iterative Methods Based on an Exponential Model for Solving Nonlinear Equations by Tianbao Liu, Hengyan Li, Zaixiang Pang

“…We present two new families of iterative methods for obtaining simple roots of nonlinear equations. …”
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Application of Homotopy Perturbation and Variational Iteration Methods for Fredholm Integrodifferential Equation of Fractional Order by Asma Ali Elbeleze, Adem Kiliçman, Bachok M. Taib

“…This paper presents the application of homotopy perturbation and variational iteration methods as numerical methods for Fredholm integrodifferential equation of fractional order with initial-boundary conditions. …”
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Effective High-Order Iterative Methods via the Asymptotic Form of the Taylor-Lagrange Remainder by Isaac Fried

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Finite Difference and Iteration Methods for Fractional Hyperbolic Partial Differential Equations with the Neumann Condition by Allaberen Ashyralyev, Fadime Dal

“…He's variational iteration method is applied. The comparison of these methods is presented.…”
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Implicit Mann Type Iteration Method Involving Strictly Hemicontractive Mappings in Banach Spaces by Arif Rafiq, Shin Min Kang

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On a Family of High-Order Iterative Methods under Kantorovich Conditions and Some Applications by S. Amat, C. Bermúdez, S. Busquier, M. J. Legaz, S. Plaza

“…This paper is devoted to the study of a class of high-order iterative methods for nonlinear equations on Banach spaces. …”
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Application of Variational Iteration Method for Dropping Damage Evaluation of the Suspension Spring Packaging System by Shuang Song, Ning-ning Duan, An-jun Chen

“…Then, a first-order approximate solution was obtained by applying He’s variable iteration method. Based on the results, a damage evaluation equation was derived, which reveals the main controlling physical parameters for damage potential of drop to packaged products concretely. …”
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An experimental comparison of two preconditioned iterative methods to solve the elliptic partial differential equations by Seyyed Ahmad Edalatpanah

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SOR-Like New Iterative Method for Solving the Epidemic Model and the Prey and Predator Problem by Atika Radid, Karim Rhofir

“…Our aim in this paper is to propose an SOR-like new iterative method by introducing a relaxation parameter ω to improve the new iterative method proposed by Daftardar-Gejji and Jafari (NIM) [J. …”
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A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators by Yong-Ju Yang, Dumitru Baleanu, Xiao-Jun Yang

“…The local fractional variational iteration method for local fractional Laplace equation is investigated in this paper. …”
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New Iterative Method for the Solution of Fractional Damped Burger and Fractional Sharma-Tasso-Olver Equations by Mohammad Jibran Khan, Rashid Nawaz, Samreen Farid, Javed Iqbal

“…The new iterative method has been used to obtain the approximate solutions of time fractional damped Burger and time fractional Sharma-Tasso-Olver equations. …”
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Solving the Fractional Rosenau-Hyman Equation via Variational Iteration Method and Homotopy Perturbation Method by R. Yulita Molliq, M. S. M. Noorani

“…We implement relatively new analytical techniques, the variational iteration method and the homotopy perturbation method, for solving this equation. …”
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