The General Hybrid Approximation Methods for Nonexpansive Mappings in Banach Spaces by Rabian Wangkeeree

“…Strong convergence theorems of the proposed iterative methods are obtained in a reflexive Banach space which admits a weakly continuous duality mapping. …”
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Asymptotic Methods for Solitary Solutions and Compactons by Ji-Huan He

“…Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter-expansion method, the Yang-Laplace transform, the Yang-Fourier transform, and ancient Chinese mathematics. …”
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Semianalytical Approach for the Approximate Solution of Delay Differential Equations by Xiankang Luo, Mustafa Habib, Shazia Karim, Hanan A. Wahash

“…The beauty of this approach is that it does not need to compute the values of the Lagrange multiplier as in the variational iteration method, and also, there is no need to implement the convolution theorem as in the Laplace transform. …”
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The Mann-Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems by Lu-Chuan Ceng, Himanshu Gupta, Ching-Feng Wen

“…These iterative algorithms are based on the regularization method, the Mann-type iteration method, and the extragradient method due to Nadezhkina and Takahashi (2006). …”
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The Equivalent Linearization Method with a Weighted Averaging for Solving Undamped Nonlinear Oscillators by D. V. Hieu, N. Q. Hai, D. T. Hung

“…The results obtained via this method are compared with the ones achieved by Parameterized Perturbation Method (PPM), Min–Max Approach (MMA), Variational Iteration Method (VIM), Homotopy Perturbation Method (HPM), Energy Balance Method (EBM), Harmonic Balance Method (HBM), 4th-Order Runge-Kutta Method, and the exact ones. …”
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Recursive Elucidation of Polynomial Congruences Using Root-Finding Numerical Techniques by M. Khalid Mahmood, Farooq Ahmad

“…For this purpose, root-finding iterative methods are employed for solving polynomial congruences of the form axn≡b(mod pk), k≥1, where a,b, and n>0 are integers which are not divisible by an odd prime p. …”
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Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method by Abdon Atangana, Adem Kılıçman

“…The method does not require any corrected function or any Lagrange multiplier and it avoids repeated terms in the series solutions compared to the existing decomposition method including the variational iteration method, the Adomian decomposition method, and Homotopy perturbation method. …”
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Numerical Solution for the 2D Linear Fredholm Functional Integral Equations by Neda Khaksari, Mahmoud Paripour, Nasrin Karamikabir

“…Using the proposed method, we get a system of linear algebraic equations which are solved by an iteration method. In the end, the accuracy and applicability of the proposed method are shown through some numerical applications.…”
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Novel Investigation of Fractional-Order Cauchy-Reaction Diffusion Equation Involving Caputo-Fabrizio Operator by Meshari Alesemi, Naveed Iqbal, Mohammed S. Abdo

“…Yang transformation is mixed with the new iteration method and homotopy perturbation method in these methods. …”
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Existence Results for a Perturbed Problem Involving Fractional Laplacians by Yan Hu

“…First, for odd nonlinearity f and for every s∈(0,1), we prove that there exists a layer solution via the monotone iteration method. Besides, existence results are obtained by variational methods for s∈(1/2,1) and for more general nonlinearities. …”
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Blow-Up Results for a Weakly Coupled System of Semilinear Wave Equations in de Sitter Spacetime by Jie Yang, Xia Ma, Caiyun Liu

“…The exponential, polynomial, and logarithmic growth of time-dependent factors in nonlinear terms are investigated by using iterative methods, respectively. Upper bound lifespan estimates of solutions to the problem are established. …”
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King-Type Derivative-Free Iterative Families: Real and Memory Dynamics by F. I. Chicharro, A. Cordero, J. R. Torregrosa, M. P. Vassileva

“…A biparametric family of derivative-free optimal iterative methods of order four, for solving nonlinear equations, is presented. …”
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The Time-Fractional Coupled-Korteweg-de-Vries Equations by Abdon Atangana, Aydin Secer

“…It was also demonstrated that HDM is more efficient than the adomian decomposition method (ADM), variational iteration method (VIM), homotopy analysis method (HAM), and homotopy perturbation method (HPM).…”
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A novel investigation of quaternion Julia and Mandelbrot sets using the viscosity iterative approach by Nabaraj Adhikari, Wutiphol Sintunavarat

“…The paper also examines how variations in the parameters of the iterative methods impact the resulting sets’ characteristics, such as shape, size, symmetry, and color.…”
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A note on computing the generalized inverse A T,S (2) of a matrix A by Xiezhang Li, Yimin Wei

“…In this note, we remove the above condition. Three types of iterative methods for A T,S (2) are presented if σ(GA|T) is a subset of the open right half-plane and they are extensions of existing computational procedures of A T,S (2), including special cases such as the weighted Moore-Penrose inverse A M,N † and the Drazin inverse AD. …”
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Thermal Elastohydrodynamic Lubrication Analysis of Point Contact for Aviation Transmission by Lu Fengxia, Long Yushi

“…The rolling bearings are widely used in the aviation transmission because of the low friction coefficient,high load ability and high reliability.It’s of great significance to study the life and contact analysis of the bearing under heavy load and severe lubrication based on the numerical analysis of thermal elastohydrodynamic lubrication（EHL） in point contact.The numerical calculation of isothermal EHL and thermal EHL models in point contact are carried out by adopting compound direct iteration method.The oil film pressure,thickness and temperature are obtained by means of Fortran,Origin and Matlab software.Synthetically considering the effect of load,speed,material and ellipticity parameter on EHL in point contact,the certain theoretical basis for heavy-load aviation transmission system is provided.…”
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Design and Kinematics Analysis of (2SPS/U)&(2SPS/RR) Type Parallel Humanoid Manipulator by Zhiguang Ma, Kangkang Wang, Leile Zhang, Shaowei Jia, Can Chen

“…The (2SPS/U)&(2SPS/RR) two-stage coupling parallel mechanism is used to drive each joint action In order to obtain its inverse and forward kinematics， the closed vector method and Newton iteration method are used to calculate the positive and negative kinematics solutions of the two-stage parallel mechanism， and then the mechanism configuration of the whole artificial arm is simplified. …”
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Comparison of Gaussian Elimination and Cholesky Decomposition Solving A Linear System Of Equation. by Nzabonimpa, Godfrey

“…Some of which are direct methods and others are iterative methods. In this work, we study direct methods specifically Gaussian elimination and Cholesky decomposition and make a comparison between the two. …”
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A Comparison of Gaussian Elimination and Cholesky Decomposition Methods in Solving a System of Linear Equations. by Niringiye, Richard

“…There are several methods of solving a system of linear equations,. some of which are direct methods and others are iterative methods. In this work, .we study direct methods specifically Gaussian elimination and Cholesky decomposition and make a comparison between the two. …”
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A Numerical Approach for the Analytical Solution of Multidimensional Wave Problems by Jinxing Liu, Jiahua Fang, Muhammad Nadeem, Yahya Alsayyad

“…Since the variational iteration method (VIM) has some assumptions and restrictions of variables during the construction of the recurrence relation, we present a Sawi integral transform for the construction of the recurrence to overcome this difficulty. …”
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