Analytical Techniques for Studying Fractional-Order Jaulent–Miodek System Within Algebraic Context by Yousuf Alkhezi, Ahmad Shafee

“…This study intends to investigate methods such as the Aboodh transform iteration method and the Aboodh residual power series method, specifically for addressing the Jaulent–Miodek system of partial differential equations. …”
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A Modified Groundwater Flow Model Using the Space Time Riemann-Liouville Fractional Derivatives Approximation by Abdon Atangana, S. C. Oukouomi Noutchie

“…The modified equation is solved via the technique of green function and the variational iteration method.…”
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A Novel Approach with Comparative Computational Simulation of Analytical Solutions of Fractional Order Volterra Type Integral Equations by Javed Iqbal, Khurram Shabbir, Liliana Guran, Homan Emadifer

“…The main purpose of this article is to reconsider the theory of variational iteration method and embed it with Laplace transform to construct the conjoined technique variational iteration Laplace transform method. …”
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Bias-free policy evaluation in the discrete-time adaptive linear quadratic optimal control in the presence of stochastic disturbances by Vina Putri Virgiani, Natsuki Ishigaki, Shiro Masuda

“…The existing deterministic policy iteration method realizes an adaptive LQ optimal regulator. …”
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Hybrid Steepest-Descent Methods for Triple Hierarchical Variational Inequalities by L. C. Ceng, A. Latif, C. F. Wen, A. E. Al-Mazrooei

“…We introduce and analyze a relaxed iterative algorithm by combining Korpelevich’s extragradient method, hybrid steepest-descent method, and Mann’s iteration method. We prove that, under appropriate assumptions, the proposed algorithm converges strongly to a common element of the fixed point set of infinitely many nonexpansive mappings, the solution set of finitely many generalized mixed equilibrium problems (GMEPs), the solution set of finitely many variational inclusions, and the solution set of general system of variational inequalities (GSVI), which is just a unique solution of a triple hierarchical variational inequality (THVI) in a real Hilbert space. …”
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Influence of Varnish on Bearing Performance and Vibration of Rotating Machinery by Chu Zhang, Jian-Gang Yang, Shi Liu, Qing-Shui Gao, Yi Yang

“…Pressure and temperature distribution were solved on the basis of the Reynolds equation by the iteration method simultaneously. It is found that bearing performance is changed by the step flow effect at the leading edge of the varnish. …”
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ACCELERATED ITERATIVE RECONSTRUCTION OF PHANTOM «ROZI» BY OS-SART METHOD USING ORDERED SUBSET PROJECTIONS by S. A. Zolotarev, M. M. Mieteeg, A. N. Al-Nadfa

“…The desire to increase the convergence rate of the iterative methods led to the use of ordered subsets of projections for both the maximum likelihood method of EM (OS-EM) and for the algebraic reconstruction method with simultaneous iterations of SART (OS-SART). …”
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Scatter and Blurring Compensation in Inhomogeneous Media Using a Postprocessing Method by Yan Yan, Gengsheng L. Zeng

“…This method also offers an alternative to compensate for scatter and blurring in a more time efficient manner compared to the popular iterative methods. The execution time for this efficient postprocessing method is only a few minutes, which is within the clinically acceptable range.…”
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Application of Gap Metric to LADRC Design in Multilinear Model of SDR by Hongfu Wang, Qinghua Zeng, An Wang, Zongyu Zhang

“…In this paper, under the LADRC frame, the gas generator system’s closed-loop stability of the SDR was analyzed and the range of compensation factors had been calculated, and then, the “gap factor” was introduced and the “cross-iteration” method was used to quickly map out the “compensation factor” in the multilinear model controller based on the variation of the zero-point position of the system and the gap metric between adjacent set points. …”
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An efficient technique to study of time fractional Whitham–Broer–Kaup equations by Nishant Bhatnagar, Kanak Modi, Lokesh Kumar Yadav, Ravi Shanker Dubey

“…Comparative numerical analyses are conducted with outcomes from the Adomian decomposition method (ADM), variational iteration method (VIM), and optimal homotopy asymptotic method (OHAM), demonstrating the superior accuracy of the proposed method. …”
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Monte Carlo Based Personalized PageRank on Dynamic Networks by Zhang Junchao, Chen Junjie, Jiancheng Song, Rong-Xiang Zhao

“…In large-scale networks, the structure of the underlying network changes frequently, and thus the power iteration method for Personalized PageRank computation cannot deal with this kind of dynamic network efficiently. …”
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Kinematical Research of Free-Floating Space-Robot System at Position Level Based on Screw Theory by Yong Wang, Xiaojun Liang, Kejie Gong, Ying Liao

“…Due to the complexity of inverse kinematical equations, a numerical method is proposed based on Newton’s iteration method. Two calculation examples are given, a dual-arm planar model and a single-arm spatial model; both forward and inverse kinematical solutions are given, while inverse kinematical results are compared with simulation results of Adams. …”
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A Three-Section-Settlement Calculation Method for Composite Foundation Reinforced by Geogrid-Encased Stone Columns by Binhui Ma, Zhiyong Hu, Zhuo Li, Kai Cai, Minghua Zhao, Chengbin He, Qiunan Chen, Bingchu Chen, Xiaocheng Huang

“…The settlement of reinforced section is calculated by the layered iteration method based on the pile element model. The compatibility of vertical and radial deformations of unreinforced section is analyzed based on the pile-soil element model. …”
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Marshall–Olkin Extended Gumbel Type-II Distribution: Properties and Applications by Farwa Willayat, Naz Saud, Muhammad Ijaz, Anita Silvianita, Mahmoud El-Morshedy

“…A simulation study is conducted using three different iterative methods with different samples of sizes n. The usefulness and potentiality of the MOEGT-II distribution have been shown using three real life data sets. …”
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Static Equilibrium Characteristics of Full-Flow Staged Combustion Cycle Engine Under Different Propellants by Haodong He, Nanjia Yu, Sihan Di, Guobiao Cai, Chuang Zhou, Lihao Zheng

“…The present study introduces an equilibrium model of the FFSC engine, utilizing the Raptor engine as a reference point and employing the discrete Newton iteration method to resolve the equilibrium equations in a fixed-point format. …”
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A Comparative Analysis of Fractional Space-Time Advection-Dispersion Equation via Semi-Analytical Methods by Noufe H. Aljahdaly, Rasool Shah, Muhammed Naeem, Mohammad Asif Arefin

“…A innovative techniques, homotopy perturbation method and new iteration method, are used in connection with the Elzaki transform to solve the “fractional advection-dispersion equation” which provides the solution in the convergent series form. …”
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Improved Newton Iterative Algorithm for Fractal Art Graphic Design by Huijuan Chen, Xintao Zheng

“…Aiming at this problem, this paper proposes an improved optimization method for selecting the initial value of the Gauss-Newton iteration method. Through the area division method of the system composed of the sensor array, the effective initial value of iterative calculation is selected in the corresponding area for subsequent iterative calculation. …”
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Transport demand as a function of the state of a transport network by T. Sakulyeva

“…They reveal the interrelation of the various steps of the modeling process and the need to use iterative methods of calculation. The functionality of the model is determined by the presence of feedbacks, which increase the ability of the model to predict actual results. …”
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Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations by Han Guo, Jun Hu, Hanru Shao, Zaiping Nie

“…To solve H-matrices system, Krylov iteration methods can be employed with appropriate preconditioners, and direct solvers based on the hierarchical structure of H-matrices are also available along with high efficiency and accuracy, which is a unique advantage compared to other fast algorithms. …”
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Joint Optimization Design of UAV-Active RIS System Based on a Quadratic Transformation by Yi Peng, Haolin Li, Qingqing Yang

“…Finally, the alternating iteration method is used to obtain the suboptimal solution of the original problem. …”
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