Analysis of Random Difference Equations Using the Differential Transformation Method by Şeyma Şişman, Mehmet Merdan

“…The differential transformation method (DTM) is one of the best methods easily applied to linear and nonlinear difference equations with random coefficients. …”
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Efficient Iterative Methods with and without Memory Possessing High Efficiency Indices by T. Lotfi, F. Soleymani, Z. Noori, A. Kılıçman, F. Khaksar Haghani

“…Two families of derivative-free methods without memory for approximating a simple zero of a nonlinear equation are presented. The proposed schemes have an accelerator parameter with the property that it can increase the convergence rate without any new functional evaluations. …”
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Transition of thermally induced flow in a square cavity using Spectral Method by Laasl Boutayna, Hilali Youssef, Mesmoudi Said, Askour Omar, Bourihane Oussama

“…The proposed algorithm integrates mesh-free Spectral methods with the Moving Collocation Element (MCOE) technique and employs a strong formulation to solve the nonlinear governing equations. Parametric analysis shows that increasing Rayleigh numbers significantly enhance the average Nusselt number, indicating a shift to convection-dominated heat transfer. …”
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The Multi-Soliton Solutions for the (2+1)-Dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada Equation by Li-Jun Xu, Zheng-Yi Ma, Jin-Xi Fei, Hui-Ling Wu, Li Cheng

“…The (2+1)-dimensional integrable Caudrey–Dodd–Gibbon–Kotera–Sawada equation is a higher-order generalization of the Kadomtsev–Petviashvili equation, which can be applied in some physical branches such as the nonlinear dispersive phenomenon. In this paper, we first present the bilinear form for this equation after constructing one Bäcklund transformation. …”
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Parameter Estimation on a Stochastic SIR Model with Media Coverage by Changguo Li, Yongzhen Pei, Meixia Zhu, Yue Deng

“…Media coverage reduces the transmission rate from infective to susceptible individuals and is reflected by suitable nonlinear functions in mathematical modeling of the disease. …”
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Bond Model of Second- and Third-Harmonic Generation in Body- and Face-Centered Crystal Structures by Hendradi Hardhienata, Tony Ibnu Sumaryada, Benedikt Pesendorfer, Adalberto Alejo-Molina

“…We also briefly discuss bulk nonlinear sources in such structures: quadrupole contribution, spatial dispersion, electric-field second-harmonic generation, and third-harmonic generation, deriving the corresponding fourth rank tensor. …”
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Motion of a Rigid Body Supported at One Point by a Rotating Arm by Jeffrey D. Stoen, Thomas R. Kane

“…This article details a scheme for evaluating the stability of motions of a system consisting of a rigid body connected at one point to a rotating arm. The nonlinear equations of motion for the system are formulated, and a method for finding exact solutions representing motions that resemble a state of rest is presented. …”
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Temperature and Pressure Dependence of the Effective Thermal Conductivity of Geomaterials: Numerical Investigation by the Immersed Interface Method by Duc Phi Do, Dashnor Hoxha

“…The present work aims to study the nonlinear effective thermal conductivity of heterogeneous composite-like geomaterials by using a numerical approach based on the immersed interface method (IIM). …”
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Existence of Periodic Solutions for a Class of Fourth-Order Difference Equation by Jia Wei, Xiaoling Han, Fumei Ye

“…We apply the continuation theorem of Mawhin to ensure that a fourth-order nonlinear difference equation of the form Δ4uk−2−akuαk+bkuβk=0 with periodic boundary conditions possesses at least one nontrivial positive solution, where Δuk=uk+1−uk is the forward difference operator, α>0,β>0 and α≠β, ak,bk are T-periodic functions and akbk>0. …”
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考虑支承跨距的非线性转子系统动力学特性研究 by 李辉, 管洪杰, 邵凤翔, 刘希东

“…According to the geometric model of spindle deformation,the total displacement relation of the front end of the spindle is obtained,and the optimum bearing span of the spindle is determined according to the minimum displacement of the front end.By means of numerical integration,the nonlinear dynamic response of the rotor system with the optimal span support is given,and the influence of rotational speed on the system dynamic response is analyzed by using axial trajectory diagram,phase portraits and Poincaré map.The results show that the rotor bearing system has good stability when it is running under the optimum support span.…”
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Robust MPPT Control of PMSG Wind Turbines Using Sliding Mode Control by Gezzaz Driss, Miqoi Sabah, El Ougli Abdelghani

“…However, due to the nonlinear nature of the system and the impact of external conditions, an effective control strategy is crucial. …”
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The Dynamic Three-Dimensional Localization of Fields in Active Percolating Systems by Gennadiy Burlak

“…Our numerical 3D simulations show that such a nonlinear system with noninteger fractal dimension has well-defined localized solutions for fields (3D speckles). …”
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Rapid Convergence for Telegraph Systems with Periodic Boundary Conditions by Peiguang Wang, Xiang Liu

“…We consider the case in which the forcing function F(t,x,U) satisfies the following condition: ∂n-1F(t,x,U)/∂Un-1 exists and is quasimonotone nondecreasing or nonincreasing. We develop nonlinear iterates of order n-1 which will be different with n being even or odd. …”
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Variation in (Hyper)Polarizability of H₂ Molecule in Bond Dissociation Processes Under Spatial Confinement by Paweł Lipkowski, Wojciech Bartkowiak

“…In contrast to the recently investigated polar LiH molecule, it was shown that the spatial confinement significantly diminishes the linear and nonlinear response of H₂ for each interatomic (H-H) distance.…”
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Existence of Positive Solutions of a Discrete Elastic Beam Equation by Ruyun Ma, Jiemei Li, Chenghua Gao

“…We consider the existence of positive solutions of the nonlinear boundary value problems of fourth-order difference equations Δ4u(t−2)−ra(t)f(u(t))=0, t∈T2, u(1)=u(T+1)=Δ2u(0)=Δ2u(T)=0, where r is a constant, a:T2→(0,∞),  and  f:[0,∞)→[0,∞) is continuous. …”
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Modified Homotopy Perturbation Method for Solving Fractional Differential Equations by A. A. Hemeda

“…The modified homotopy perturbation method is extended to derive the exact solutions for linear (nonlinear) ordinary (partial) differential equations of fractional order in fluid mechanics. …”
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Fractal Dynamics and Control of the Fractional Potts Model on Diamond-Like Hierarchical Lattices by Weihua Sun, Shutang Liu

“…To associate two different Julia sets of the fractional model with different parameters and fractional orders, nonlinear coupling items are taken to make one Julia set change to another. …”
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Assessment of six insulin resistance surrogate indexes for predicting stroke incidence in Chinese middle-aged and elderly populations with abnormal glucose metabolism: a nationwide... by Luqing Jiang, Tengxiao Zhu, Wenjing Song, Ying Zhai, Yu Tang, Fengxia Ruan, Zichen Xu, Lei Li, Xia Fu, Daoqin Liu, Aidong Chen, Qiwen Wu

“…Dose-response analyses showed that eGDR, CVAI, TyG-BMI and METS-IR were linearly associated with stroke risk (P nonlinear ≥ 0.05), whereas TyG and AIP were nonlinearly associated with stroke risk (P nonlinear < 0.05). …”
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On Some Metric Inequalities and Applications by Hassen Aydi, Bessem Samet

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Optimal Control of a Viscous Shallow Water Equation by Wenbin Zhang, Jiangbo Zhou

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