Dynamics Simulation of the Tooth Root Crack Fault of Gear Transmission System by Ning Shaohui, Han Zhennan, Li Yuexian, Wu Xuefeng

“…By using the Matlab,the dynamics differential equations of the model are solved,the angular velocity and angular acceleration simulation curve of the two kinds of fault and intact gear are got,the result is that the gear turning crack,angular velocity and angular acceleration of the driven produced obvious fluctuations,the calculation results are consistent with theoretical analysis.…”
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Investigation of a spatial double pendulum: an engineering approach by S. Bendersky, B. Sandler

“…Matlab computer programs were used for solving the nonlinear differential equations by the Runge-Kutta method. Fourier transformation was used to obtain the frequency spectra for analyses of the oscillations of the two pendulums. …”
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New Exact Solutions of Kolmogorov Petrovskii Piskunov Equation, Fitzhugh Nagumo Equation, and Newell-Whitehead Equation by Yu-Ming Chu, Shumaila Javeed, Dumitru Baleanu, Sidra Riaz, Hadi Rezazadeh

“…This work presents the new exact solutions of nonlinear partial differential equations (PDEs). The solutions are acquired by using an effectual approach, the first integral method (FIM). …”
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SIMULATION OF OPEN MECHANISMS FOR THE ADDITIVE PROCESS WELD PLASTICS by N. N. Hurski, V. A. Skachek, A. V. Skachek, Y. A. Skudnyakov

“…This article discusses: model of the two-link mechanism; generalized scheme of mechatronic simulation model of 3D-printer with the positioning units of electric DC; mathematical model of the actuator of the printer unit in the form of a system of differential equations; 3D-printer programming model implemented in the Matlab-Simulink environment using the c standard library blocks and SimMechanics library; virtual (animated) 3D printer model on the basis of the library Simulink 3D Animation, supports the visualization of the movements of the designed mechanism of the basic units. …”
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The numerical models of the estimation of the electrooptical parameters of GaAs by Albertas Pincevičius, Rimantas-Jonas Rakauskas, Svajonė Vošterienė

“…The system of the differential equations was solved by a method Gear with a modification of a step. …”
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Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem by R. J. Moitsheki, M. D. Mhlongo

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Modeling and Dynamics Characteristic Analysis of Helical Gear System with Considering Tooth Surface Friction by Kang Boqiang, Gou Xiangfeng

“…The movement differential equations are discussed by the variable step size Runge- Kutta method. …”
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Mode Transition Phenomenon of Herringbone Gear Power-split Transmission System by Jincheng Dong, Sanmin Wang

“…The torsional vibration model and the free torsional vibration differential equations of the herringbone gear power-split transmission system are established， and the torsional vibration models are classified to two kinds of the coupled vibration mode and the branch gear vibration model by calculating the torsional vibration natural frequency and vibration mode. …”
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Optical vortices in dispersive nonlinear Kerr-type media by Lubomir M. Kovachev

“…The applied method of slowly varying amplitudes gives us the possibility to reduce the nonlinear vector integrodifferential wave equation of the electrical and magnetic vector fields to the amplitude vector nonlinear differential equations. Using this approximation, different orders of dispersion of the linear and nonlinear susceptibility can be estimated. …”
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Dynamic Analysis on a Diffusive Two-Enterprise Interaction Model with Two Delays by Yanxia Zhang, Long Li

“…In addition, the direction of Hopf bifurcation and the stability of the periodic solutions are discussed by using the normal form theory and the center manifold reduction of partial functional differential equations. Finally, numerical simulation experiments are conducted to illustrate the validity of the theoretical conclusions.…”
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Conservation Laws, Symmetry Reductions, and New Exact Solutions of the (2 + 1)-Dimensional Kadomtsev-Petviashvili Equation with Time-Dependent Coefficients by Li-hua Zhang

“…Applying the characteristic equations of the obtained symmetries, the (2 + 1)-dimensional KP equation is reduced to (1 + 1)-dimensional nonlinear partial differential equations, including a special case of (2 + 1)-dimensional Boussinesq equation and different types of the KdV equation. …”
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Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals by Aneta Sikorska-Nowak

“…We prove existence theorems for integro-differential equations 𝑥Δ∫(𝑡)=𝑓(𝑡,𝑥(𝑡),𝑡0𝑘(𝑡,𝑠,𝑥(𝑠))Δ𝑠), 𝑥(0)=𝑥0, 𝑡∈𝐼𝑎=[0,𝑎]∩𝑇, 𝑎∈𝑅+, where 𝑇 denotes a time scale (nonempty closed subset of real numbers 𝑅), and 𝐼𝑎 is a time scale interval. …”
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ON APPLICATION OF ARTIFICIAL NEURAL NETWORKS FOR MODELING OF WATER CONSUMPTION by Alexander N. Salugin, Roman N. Balkushkin

“…The use of mathematical models in the form of a system of differentiated equations is hampered by the uncertainty of the coefficients in their right-hand sides, which describe the intensities of processes of different natures: precipitation, water consumption by various sectors of the water management complex, water runoff during snow melting, transpiration, infiltration, etc. …”

Research of Flexible Multibody Dynamics Modeling of Conveyor Belt by Wang Fansheng

“…Based on Lagrange equations of the second kind,the dynamics differential equations of rigid elements are established. …”
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BUCKLING OF BEAMS WITH A BOUNDARY ELEMENT TECHNIQUE by ABDERRAZEK MESSAOUDI, LASZLO PETER KISS

“…If the Green functions of these boundary value problems are known, the differential equations of the stability problems that contain the critical load sought can be turned into eigenvalue problems given by homogeneous Fredholm integral equations. …”
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Limit Cycles of a Class of Perturbed Differential Systems via the First-Order Averaging Method by Amor Menaceur, Salah Mahmoud Boulaaras, Amar Makhlouf, Karthikeyan Rajagobal, Mohamed Abdalla

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Solving Quantum Dynamics with a Lie-Algebra Decoupling Method by Sofia Qvarfort, Igor Pikovski

“…The approach involves identifying a Lie algebra that governs the dynamics of the system, enabling the derivation of differential equations to solve the Schrödinger equation. …”
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Group Classification of a Generalized Lane-Emden System by Ben Muatjetjeja, Chaudry Masood Khalique, Fazal Mahmood Mahomed

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Stability Analysis of a Class of Neural Networks with State-Dependent State Delay by Yue Chen, Jin-E Zhang

“…The differential equations with state-dependent delay are very important equations because they can describe some problems in the real world more accurately. …”
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The Approximate Solution of Some Plane Boundary Value Problems of the Moment Theory of Elasticity by Roman Janjgava

“…We consider a two-dimensional system of differential equations of the moment theory of elasticity. …”
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