Effects of Elastic Foundation on the Vibration of Laminated Non-Homogeneous Orthotropic Circular Cylindrical Shells by A.H. Sofiyev, S.N. Keskin, Ali H. Sofiyev

“…Applying Galerkin method to the latter equations, a non-linear time dependent differential equation is obtained for the displacement amplitude. …”
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Thermal performance of a moving fin with temperature-dependent thermal conductivity in convective and radiative environment by Yanqun Han, Xulong Peng

“…It corresponds to a nonlinear heat transfer problem related to the nonlinear ordinary differential equation (NODE) for the unknown temperature excess. …”
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Study on the Load Sharing Characteristic and Influential Factor of the Planetary Transmission of Vertical Mill Reducer by Wang Wuguang

“…Taking planetary gear pair time-meshing stiffness,meshing damping,bearing support stiffness,support damping of vertical mill reducer into consideration,the vibration differential equation of planetary gear transmission is set up based on lumped parameter method,the dynamic mesh force of each gear pair is obtained by adopting Runge-Kutta method. …”
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Mathematical Model of Pipeline Abandonment and Recovery in Deepwater by Xia-Guang Zeng, Meng-Lan Duan, Chen An

“…For this problem a third-order differential equation is used as the governing equation in this paper, rather than the traditional second-order one. …”
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Shaping Single Offset Reflector Antennas Using Local Axis-Displaced Confocal Quadrics by Rafael A. Penchel, José R. Bergmann, Fernando J. S. Moreira

“…This work investigates a novel numerical procedure for the solution of an exact formulation for the Geometrical Optics synthesis of a single reflector antenna by simultaneously imposing Snell’s Law and Conservation of Energy in a tube of rays, yielding a second-order nonlinear partial differential equation of Monge-Ampère type, which can be solved as a boundary value problem. …”
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Dynamics of a Single Species in a Fluctuating Environment under Periodic Yield Harvesting by Mustafa Hasanbulli, Svitlana P. Rogovchenko, Yuriy V. Rogovchenko

“…We discuss the effect of a periodic yield harvesting on a single species population whose dynamics in a fluctuating environment is described by the logistic differential equation with periodic coefficients. This problem was studied by Brauer and Sánchez (2003) who attempted the proof of the existence of two positive periodic solutions; the flaw in their argument is corrected. …”
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The Impacts of Reducing the Infection Rate and Infection Source on the Transmission of Emerging Infectious Diseases by Jia-Tong Li

“…The impacts of measures intensity, diagnosis rate, and the start time of taking measures on emerging infectious diseases with infectious capacity during the incubation period are considered comprehensively by using a differential equation model. Results show that for each diagnosis rate, the number of infections and deaths has a phase change structure with respect to the measures intensity. …”
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Stiffness Calculation for Negative Moment Region of Steel-Concrete Composite Beams considering the Influence of Cracking and Interface Slip by Wenlong Cao, Jianqing Bu, Cunbao Zhao, Xueyan Wang, Liping Zhang, Jiren Zhang

“…To evaluate this decrease in the stiffness of SCCBs, a static differential equation is used to derive analytical expressions of interface slip and deflection. …”
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Modal Perturbation Method for the Dynamic Characteristics of Timoshenko Beams by Menglin Lou, Qiuhua Duan, Genda Chen

“…In this approach, the differential equation of motion describing the dynamic behavior of the Timoshenko beam can be transformed into a set of nonlinear algebraic equations. …”
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Kinetic Analysis for Macrocyclizations Involving Anionic Template at the Transition State by Vicente Martí-Centelles, M. Isabel Burguete, Santiago V. Luis

“…The corresponding differential equation systems for each kinetic model can be solved numerically. …”
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A Model for Service Life Control of Selected Device Systems by Zieja Mariusz, Ważny Mariusz

“…For estimation of deviation increasing rate in probabilistic sense, was used a difference equation from which, after transformation, Fokker-Planck differential equation was obtained [4, 11]. A particular solution of the equation is deviation increasing rate density function which was used for determining exceedance probability of limit state. …”
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Analysis of Complex Modal Characteristics of Fractional Derivative Viscoelastic Rotating Beams by Tianle Lu, Zhongmin Wang, Dongdong Liu

“…For the transverse vibration problem of a fractional derivative viscoelastic rotating beam, the differential equation of the system is obtained based on the Euler–Bernoulli beam theory and Hamilton principle. …”
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A Finite Difference Scheme for Pricing American Put Options under Kou's Jump-Diffusion Model by Jian Huang, Zhongdi Cen, Anbo Le

“…By adding a penalty term, the partial integrodifferential complementarity problem arising from pricing American put options under Kou's jump-diffusion model is transformed into a nonlinear parabolic integro-differential equation. Then a finite difference scheme is proposed to solve the penalized integrodifferential equation, which combines a central difference scheme on a piecewise uniform mesh with respect to the spatial variable with an implicit-explicit time stepping technique. …”
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Flow between caoxial rotating disks: with and without externally applied magnetic field by R. K. Bhatnagar

“…The governing system of a pair of non-linear ordinary differential equation is solved by treating Reynolds number to small. …”
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PRIMARY RESONANCE ANALYSIS OF ARM SYSTEM UNDER BOUNDED NARROW⁃BAND EXCITATION by YANG ZhiAn, MAN ZhiJun, LIU WenYang

“…By using multi⁃scales method,the first primary resonance of the human arm and vibration mechanical coupling system under random narrow⁃band excitation was analyzed,and the two⁃degree⁃of⁃freedom nonlinear dynamic equation of the arm system was established.The first primary resonance amplitude frequency response equation and Ito stochastic differential equation of the system were solved in turn.In order to study the distribution law of variables under random vibration,the approximate expressions of the expectation and mean square value of the first primary resonance random mean square response were calculated using the moment estimation method.The influence of the parameters of the human arm system on the primary resonance was obtained through numerical analysis.The results show that the mean square response curves of the first primary resonance have the same topological structure as their amplitude⁃frequency response curves,and the mean square value of the primary resonance amplitudes and the resonance region increase with the increase of the amplitude of the external excitation,while the increase of the system damping will reduce the mean square value and the resonance region.The change of nonlinear stiffness coefficient has little effect on the system.…”
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Mathematical models of contact patterns between age groups for predicting the spread of infectious diseases by Sara Y. Del Valle, J. M. Hyman, Nakul Chitnis

“…The spread of an infectious disease is sensitive to the contact patterns in the population and to precautions people take to reduce the transmission of the disease.We investigate the impact that different mixing assumptions have on the spread an infectious disease in an age-structured ordinary differential equation model. We consider the impact of heterogeneity in susceptibility and infectivity within the population on the disease transmission. …”
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High-Accurate Numerical Schemes for Black–Scholes Models with Sensitivity Analysis by Samir Kumar Bhowmik, Jakobin Alam Khan

“…The significance of both the linear and nonlinear Black-Scholes partial differential equation model is huge in the field of financial analysis. …”
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Numerical Solution of the 1D Advection-Diffusion Equation Using Standard and Nonstandard Finite Difference Schemes by A. R. Appadu

“…Three numerical methods have been used to solve the one-dimensional advection-diffusion equation with constant coefficients. This partial differential equation is dissipative but not dispersive. …”
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Super algebra and Harmonic Oscillator in Anti de Sitter space by Omid Jalili, Shahin Toni

“…Then we apply the supersymmetric Quantum Mechanics approach to solve our differential equation. In this paper we have solved Schrodinger equation for harmonic oscillator in AdS spacetime by supersymmetry approach. …”
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The Cigar-Shaped Background Metric with Supersymmetry Approaches and Thermal Properties of System by Omid Jalili, Shahin Toni, Jafar Sadeghi

“…SUSY quantum mechanics can be used to solve ordinary differential equation. Using this method, we obtained the energy spectrum of the Fermions on the aforementioned background. …”
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