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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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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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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New Numerical Solution of von Karman Equation of Lengthwise Rolling by Rudolf Pernis, Tibor Kvackaj

“…The contribution of the present paper for solution of two-dimensional differential equation of rolling is based on description of the circular arch by equation of a circle. …”
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Study on dynamics characteristic on combination misalignment and rubbing of the dual-rotor system by YAO Xia, NAN Guofang, LI Yao, QIU Xuewen

“…The misalignment of the dual-rotor system for the aero-engine will lead to abnormal increase of the vibration which results in the rotor-stator rubbing and affects the safty and stability of the rotor operation.The dual-rotor system was taken as the research object.Considering the combination misalignment-rubbing fault, the dynamic model of the rotor system is established based on the lumped mass method.The differential equation of the system motion was established according to the Lagrange equation, and the Range-Kutta method was used to solve it.The influence mechanism of the key parameters such as the speed, the misalignment angle and the coupling misalignment on the nonlinear dynamic characteristics of the system was studied.The results show that the system presents complex dynamic characteristics such as periodic, multi-periodic, quasi-periodic and chaotic motion with the increase of the rotor’s speed.When the speed is in the range of 1 500-2 200 rad/s, the system switches between periodic 2 motion and chaotic state through multiple paroxysmal bifurcations and paroxysmal inverted bifurcations.There are nonlinear phenomena such as jump in the bifurcation diagram of the vibration response with the change of the parallel misalignment of the coupling.As the misalignment angle of the bearing increases, the chaotic interval of the high speed decreases, and the stable periodic motion interval increases.…”
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A Solution of the Complex Fuzzy Heat Equation in Terms of Complex Dirichlet Conditions Using a Modified Crank–Nicolson Method by Hamzeh Zureigat, Mohammad A. Tashtoush, Ali F. Al Jassar, Emad A. Az-Zo’bi, Mohammad W. Alomari

“…This study explores complex fuzzy numbers and introduces their application for the first time in the literature to address a complex fuzzy partial differential equation that involves a complex fuzzy heat equation under Hukuhara differentiability. …”
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Parametric Study on the Influence of Warping Deformation upon Natural Frequencies of Die Springs by Ying Hao, Junfeng Guan

“…The warping deformation of spring’s cross section, as a new design factor, is incorporated into the differential equation of motion. Numerical simulations show that the warping deformation is a significant role of the behavior of natural frequencies of die springs and should be considered carefully. …”
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Brock's approaching zero method improved as approaching fixed point frequency to solve optimum damping ratio of dynamic vibration absorber in machine tools and experimental confirm... by Hongliang Tian, Xixiao Liang, Xuan Du

“…Some exact closed-form solutions, for example displacement amplitude gain, fixed point coordinate, and optimum damping ratio, were deduced with the real number form of differential equation of load motion and employing L'Hospital first rule. …”
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Analytical Solutions to Two-Dimensional Nonlinear Telegraph Equations Using the Conformable Triple Laplace Transform Iterative Method by Alemayehu Tamirie Deresse

“…According to the findings, the proposed method is being used to solve additional forms of nonlinear fractional partial differential equation systems. Moreover, the conformable fractional triple Laplace transform iterative method has a small computational size as compared to other methods.…”
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Interval Shannon Wavelet Collocation Method for Fractional Fokker-Planck Equation by Shu-Li Mei, De-Hai Zhu

“…Then, combining with the finite difference technology, a new numerical method for the time fractional partial differential equation is constructed. A simple Fokker-Planck equation is taken as an example to illustrate the effectiveness by comparing with the Grunwald-Letnikov central difference approximation (GL-CDA).…”
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Combined Damped Sinusoidal Oscillation Solutions to the (3 + 1)-D Variable-Coefficient Generalized NLW Equation in Liquid with Gas Bubbles by Xiuwang Wang, Jalil Manafian, Wayan Eka Mahendra, Azher M. Abed, Mustafa Z. Mahmoud, Guizhen Liang

“…The damped sinusoidal oscillations for two cases of the nonlinear wave ordinary differential equation will be studied. Using suitable mathematical assumptions, the novel kinds of solitary, periodic, and singular soliton solutions are derived and established in view of the trigonometric and rational functions of the governing equation. …”
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Research on the Trajectory Model for ZY-3 by Yifu Chen, Zhong Xie

“…Meanwhile, the differential equation is derivate for the bundle block adjustment. …”
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Mathematical modeling of Glassy-winged sharpshooter population by Jeong-Mi Yoon, Volodymyr Hrynkiv, Lisa Morano, Anh Tuan Nguyen, Sara Wilder, Forrest Mitchell

“…The model is a delayGompertz differential equation with harvesting and immigrationterms, and we use the data to estimate the model parameters.…”
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Symmetry analysis, dynamical behavior, and conservation laws of the dual-mode nonlinear fluid model by Adil Jhangeer, Beenish, Lubomír Říha

“…Lie theory converts the equation into a nonlinear ordinary differential equation using similarity variables. The model is transformed into a planar dynamical system via Galilean transformation, with phase portraits generated using bifurcation parameters. …”
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Network-level reproduction number and extinction threshold for vector-borne diseases by Ling Xue, Caterina Scoglio

“…Relationships between basic reproduction numbers of two deterministic network-based ordinary differential equation vector-host models, and extinction thresholds of corresponding stochastic continuous-time Markov chain models are derived under some assumptions. …”
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Urban Lead: Modeling Its Distribution and Effects on Children by Zhixiong Chen, Yi Ding, Andrew Getz, Bernard Lipat

“…The model is constructed using the diffusion-advection partial differential equation in three spatial dimensions and one temporal dimension with an initial condition and boundary conditions. …”
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Dynamics of evolutionary competition between budding and lytic viral release strategies by Xiulan Lai, Xingfu Zou

“…In this paper, we consider the evolutionary competition between budding and lytic viral release strategies, using a delay differential equation model with distributed delay. When antibody is not established, the dynamics of competition depends on the respective basic reproductive ratios of the two viruses. …”
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A Strength Design Method of Cemented Backfill with a High Aspect Ratio by Zhi-zhihui Wang, Ai-xiang Wu, Hong-jiang Wang

“…Then, by the combination of the minor principal stress trajectory method and the horizontal slice method, an ordinary differential equation of stresses was established and then solved numerically. …”
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Mathematical model of penetration of cylindrical electromagnetic fields with axial symmetry through the plane screen from permalloy by V. Т. Erofeenko

“…The boundary-value problem is based on the use of differential Maxwell equations and complementary nonlinear differential equation for the field of magnetization, characterizing the permalloy. …”
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