Improved Riccati Transfer Matrix Method for Free Vibration of Non-Cylindrical Helical Springs Including Warping by A.M. Yu, Y. Hao

“…Free vibration equations for non-cylindrical (conical, barrel, and hyperboloidal types) helical springs with noncircular cross-sections, which consist of 14 first-order ordinary differential equations with variable coefficients, are theoretically derived using spatially curved beam theory. …”
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Application of Fuzzy Fractional Kinetic Equations to Modelling of the Acid Hydrolysis Reaction by Ferial Ghaemi, Robiah Yunus, Ali Ahmadian, Soheil Salahshour, Mohamed Suleiman, Shanti Faridah Saleh

“…The method is computationally interesting, and the numerical results demonstrate the effectiveness and validity of the method for solving fuzzy fractional differential equations.…”
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Vibration Characteristics for Moving Printing Membrane with Variable Density along the Lateral Direction by Mingyue Shao, Jimei Wu, Yan Wang, Qiumin Wu, Yuan Chen

“…The transverse vibration differential equations of moving membrane are established based on D’Alembert’s principle and discretized by using the differential quadrature method (DQM). …”
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Analysis of Nonlinear Structural Dynamics and Resonance in Trees by H. Doumiri Ganji, S.S. Ganji, D.D. Ganji, F. Vaseghi

“…Many of such nonlinear differential equations are complicated to solve. Therefore, this paper focuses on an accurate and simple solution, Differential Transformation Method (DTM), to solve the derived equation. …”
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A High Accuracy Spatial Reconstruction Method Based on Surface Theory for Regional Ionospheric TEC Prediction by Jian Wang, Yi‐ran Liu, Ya‐fei Shi

“…The core theory of this method is as follows: (a) Any surface can be uniquely determined by its first and second fundamental quantities; (b) By direct difference approximation, differential equations are transformed into algebraic equations to solve Gauss equations faster. …”
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Mathematical modeling predicts that endemics by generalist insects are eradicated if nearly all plants produce constitutive defense by Suman Chakraborty, Shalu Dwivedi, Stefan Schuster

“…The objective is addressed by developing deterministic ordinary differential equations under the following conditions: Plants without constitutive defenses are susceptible to oviposition by generalist insects, while they become defended against generalists by storing chemical defenses. …”
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Identification of a simplified mathematical model of an unmanned aerial vehicle by A. A. Lobaty, Y. F. Yatsyna, S. S. Prohorovith, Y. A. Hvitko

“…The analytical substantiation of the need to apply the methods of linearization of the mathematical model of UAV movement and the accepted assumptions for obtaining differential equations of UAV movement relative to the center of mass, allowing to synthesize the required transfer function of the corresponding element of the UAV control system. …”
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A Strongly A-Stable Time Integration Method for Solving the Nonlinear Reaction-Diffusion Equation by Wenyuan Liao

“…The semidiscrete ordinary differential equation (ODE) system resulting from compact higher-order finite difference spatial discretization of a nonlinear parabolic partial differential equation, for instance, the reaction-diffusion equation, is highly stiff. …”
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Advanced Method for Calculations of Core Burn-Up, Activation of Structural Materials, and Spallation Products Accumulation in Accelerator-Driven Systems by A. Stankovskiy, G. Van den Eynde

“…Secondly, it uses a state-of-the-art numerical solver for the first-order ordinary differential equations describing the isotope balances, namely, a Radau IIA implicit Runge-Kutta method. …”
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On Modeling and Constrained Model Predictive Control of Open Irrigation Canals by Lihui Cen, Ziqiang Wu, Xiaofang Chen, Yanggui Zou, Shaohui Zhang

“…As a set of hyperbolic partial differential equations, they are not solved explicitly and difficult to design optimal control algorithms. …”
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The Hadamard-PINN for PDE inverse problems: Convergence with distant initial guesses by Yohan Chandrasukmana, Helena Margaretha, Kie Van Ivanky Saputra

“…This paper presents the Hadamard-Physics-Informed Neural Network (H-PINN) for solving inverse problems in partial differential equations (PDEs), specifically the heat equation and the Korteweg–de Vries (KdV) equation. …”
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Differential Games of Rechargeable Wireless Sensor Networks against Malicious Programs Based on SILRD Propagation Model by Guiyun Liu, Baihao Peng, Xiaojing Zhong, Xuejing Lan

“…In this paper, nodes are divided into five states according to the residual energy and infection level, and the differential equations are constructed to describe the evolution of nodes. …”
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Resolvent Positive Operators and Positive Fractional Resolvent Families by Nan-Ding Li, Ru Liu, Miao Li

“…Some examples of positive solutions to fractional differential equations are presented to illustrate our results.…”
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Prediction of Shear Lag Effect in Thin-Walled Single-Box Multicell Box Girder Based on the Modified Warping Displacement Function by Xiayuan Li, Shui Wan, Kongjian Shen, Peng Zhou, Xiao Wang

“…Based on the principle of minimum potential energy, the governing differential equations are derived and solved with the associated boundary and load conditions. …”
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The Quantum Analysis of Nonlinear Optical Parametric Processes with Thermal Reservoirs by Tamirat Abebe, Nebiyu Gemechu, Chimdessa Gashu, Kebede Shogile, Solomon Hailemariam, Shimelis Adisu

“…In this paper, employing the stochastic differential equations associated with the normal ordering, the quantum properties of a nondegenerate three-level cascade laser with a parametric amplifier and coupled to a two-mode thermal reservoir are thoroughly analyzed. …”
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Dynamic Response of Parallel Hoisting System under Drive Deviation between Ropes with Time-Varying Length by Guohua Cao, Xiang Cai, Naige Wang, Weihong Peng, Jishun Li

“…The slack situation of the rope is considered, and the dynamic equations which are systems of DAEs are transformed to ordinary differential equations (ODEs). The dynamic responses of tension, torsion, and acceleration are analyzed considering radius’ error of the drums, which indicates that the drive deviation between ropes can cause large influence on the tension difference and even cause one of the ropes to slack. …”
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Models for the spread and persistence of hantavirus infection in rodents with direct and indirect transmission by Curtis L. Wesley, Linda J. S. Allen, Michel Langlais

“…Two models are analyzed, a nonautonomous system of differential equations with time-periodic coefficients and an autonomous system, where the coefficients are taken to be the time-average. …”
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Global dynamics of a simple model for wild and sterile mosquitoes by Yu Ichida, Yukihiko Nakata

“…Then, the global behavior of the solution of the two-dimensional ordinary differential equation system is classified in a two-parameter plane represented by the natural death rate of mosquitoes and the sterile mosquito release rate. …”
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Nonlinear Hydroelastic Waves beneath a Floating Ice Sheet in a Fluid of Finite Depth by Ping Wang, Zunshui Cheng

“…The present formulas, different from the perturbation solutions, are highly accurate and uniformly valid without assuming that these nonlinear partial differential equations (PDEs) have small parameters necessarily. …”
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Hydrodynamic Boundary Layer Flow of Chemically Reactive Fluid over Exponentially Stretching Vertical Surface with Transverse Magnetic Field in Unsteady Porous Medium by M. Sulemana, I. Y. Seini, O. D. Makinde

“…The flow problem is modelled as time depended dimensional partial differential equations which are transformed to dimensionless equations and solved by means of approximate analytic method. …”
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