A Nonlinear Fractional Problem with a Second Kind Integral Condition for Time-Fractional Partial Differential Equation by Benbrahim Abdelouahab, Taki-Eddine Oussaeif, Adel Ouannas, Khaled M. Saad, Hadi Jahanshahi, Ahmed Diar, Awad M. Aljuaid, Ayman A. Aly

“…For this aim, we split the proof into two parts; to study the main linear problem part, we used the variable separation method, and concerning the semilinear problem part, we apply an iterative method and a priori estimate for the study of the weak solution.…”
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A Numerical Approach to Static Deflection Analysis of an Infinite Beam on a Nonlinear Elastic Foundation: One-Way Spring Model by Jinsoo Park, Hyeree Bai, T. S. Jang

“…The nonlinear procedure involves Green’s function technique and an iterative method using the pseudo spring coefficient. The workability of the numerical procedure is demonstrated through showing the validity of the solution and the convergence test with some external loads.…”
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Solving a Class of Singular Fifth-Order Boundary Value Problems Using Reproducing Kernel Hilbert Space Method by Yulan Wang, Shuai Lu, Fugui Tan, Mingjing Du, Hao Yu

“…The approximate solution is given by using an iterative method and the finite section method. The present method reveals to be more effective and convenient compared with the other methods.…”
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A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions by Taohua Liu, Muzhou Hou

“…Then, we present a fast iterative method for the implicit finite difference scheme, which only requires storage of O(K) and computational cost of O(Klog⁡K). …”
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Modeling of Unsteady Sheet Cavitation on Marine Propeller Blades by Spyros A. Kinnas, HanSeong Lee, Yin L. Young

“…The time-dependent extent and thickness of the cavity were determined by using an iterative method. The cavity detachment was determined by applying the smooth detachment criterion in an iterative manner. …”
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Numerical Simulation of Fractional Zakharov–Kuznetsov Equation for Description of Temporal Discontinuity Using Projected Differential Transform Method by Dianchen Lu, Muhammad Suleman, Jamshaid Ul Rahman, Samad Noeiaghdam, Ghulam Murtaza

“…The core aim of this study is to propose a novel computational procedure, namely, Elzaki transform iterative method to work out two-dimensional nonlinear time-fractional Zakharov–Kuznetsov equation numerically. …”
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Self-Adaptive Predictor-Corrector Approach for General Variational Inequalities Using a Fixed-Point Formulation by Kubra Sanaullah, Saleem Ullah, Muhammad Shoaib Arif, Kamaleldin Abodayeh, Rabia Fayyaz

“…We introduced a new iterative method based on a self-adaptive predictor-corrector approach for finding a solution to the GVI. …”
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Numerical Study of Natural Convection in a Heated Enclosure with Two Wavy Vertical Walls Using Finite Element Method by Pensiri Sompong, Supot Witayangkurn

“…The wavy enclosure is transformed to a unit square in the computational domain and the finite element formulations are solved in terms of ξη-coordinate based on iterative method. In order to investigate the effects of interested parameters, the values of wave amplitude (λ = 0.05 and 0.1) and number of undulations (n = 1 and 2) are chosen with constants Ra = 105, Da = 10−3, and Pr = 0.71. …”
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Study on the Coupling Frequency of Double-Sided Submerged Ring-Stiffened Cylindrical Shells by Anbin Yu, Yinglong Zhao, Youqian Wang, Ben Zhang

“…Muller three-point iterative method is used to solve the coupling frequency. …”
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Pricing of American Put Option under a Jump Diffusion Process with Stochastic Volatility in an Incomplete Market by Shuang Li, Yanli Zhou, Xinfeng Ruan, B. Wiwatanapataphee

“…By employing a risk-minimization criterion, we obtain the Radon-Nikodym derivative for the minimal martingale measure and consequently a linear complementarity problem (LCP) for American option price. An iterative method is then established to solve the LCP problem for American put option price. …”
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Reduction of Free Edge Peeling Stress of Laminated Composites Using Active Piezoelectric Layers by Bin Huang, Heung Soo Kim

“…The approach is the extended Kantorovich method which is an iterative method. Multiterms of trial function are employed and governing equations are derived by taking the principle of complementary virtual work. …”
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Three-Step Block Method for Solving Nonlinear Boundary Value Problems by Phang Pei See, Zanariah Abdul Majid, Mohamed Suleiman

“…The proposed block method will be adapted with multiple shooting techniques via the three-step iterative method. The boundary value problem will be solved without reducing to first-order equations. …”
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Inverse Numerical Iterative Technique for Finding all Roots of Nonlinear Equations with Engineering Applications by Mudassir Shams, Naila Rafiq, Babar Ahmad, Nazir Ahmad Mir

“…We introduce here a new two-step derivate-free inverse simultaneous iterative method for estimating all roots of nonlinear equation. …”
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Comparison of Different Analytic Solutions to Axisymmetric Squeezing Fluid Flow between Two Infinite Parallel Plates with Slip Boundary Conditions by Hamid Khan, S. Islam, Javed Ali, Inayat Ali Shah

“…The velocity profiles are investigated through various analytical techniques like Adomian decomposition method, new iterative method, homotopy perturbation, optimal homotopy asymptotic method, and differential transform method.…”
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Input-to-State Stabilization of a Class of Uncertain Nonlinear Systems via Observer-Based Event-Triggered Impulsive Control by Xiangru Xing, Jin-E Zhang

“…By resorting to the iterative method and Lyapunov technology, some sufficient criteria are established to guarantee the input-to-state stability of the newly uncertain controlled system under the employed controller, in which an innovative approximation condition as to the uncertain term is proposed and the linear matrix inequality technique is utilized for restraining sophisticated parameter uncertainties. …”
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A Two-Level Iterative Node Importance Evaluation of Aircraft Function Modules Based on Influence Matrix by Chang Liu, Jinyan Wang, Kangxing Wang

“…In view of this situation, this paper researches the two-level iterative method of evaluating the importance of aircraft function modules. …”
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Optimal Sixteenth Order Convergent Method Based on Quasi-Hermite Interpolation for Computing Roots by Fiza Zafar, Nawab Hussain, Zirwah Fatimah, Athar Kharal

“…We have given a four-step, multipoint iterative method without memory for solving nonlinear equations. …”
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A Discrete Mathematical Modeling and Optimal Control of the Electoral Behavior with regard to a Political Party by Omar Balatif, Abderrahim Labzai, Mostafa Rachik

“…Pontryagin’s Maximum Principle, in discrete time, is used to characterize the optimal controls and the optimality system is solved by an iterative method. The numerical simulation is carried out using Matlab. …”
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Prevention of Leptospirosis Infected Vector and Human Population by Multiple Control Variables by Muhammad Altaf Khan, Saeed Islam, Sher Afzal Khan, Ilyas Khan, Sharidan Shafie, Taza Gul

“…We completely characterize the optimal control problem and compute the numerical solution of the optimality system using an iterative method.…”
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Vortex-Induced Vibration Suppression of Bridges by Inerter-Based Dynamic Vibration Absorbers by Junjie Chen, Michael Z. Q. Chen, Yinlong Hu

“…The performance indexes for the vertical displacement of six IDVA arrangements are obtained by using an iterative method, where the performance indexes for the vertical displacement are minimized by using the optimization toolbox in a commercial software. …”
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