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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A Numerical Method for Time-Fractional Reaction-Diffusion and Integro Reaction-Diffusion Equation Based on Quasi-Wavelet by Sachin Kumar, Jinde Cao, Xiaodi Li

“…In this research work, we focused on finding the numerical solution of time-fractional reaction-diffusion and another class of integro-differential equation known as the integro reaction-diffusion equation. …”
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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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Optimal investment game for two regulated players with regime switching by Lin Xu, Linlin Wang, Hao Wang, Liming Zhang

“…In the first case, the associated Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation was an elliptic partial differential equation (PDE). By solving an auxiliary problem, we demonstrated the existence and regularity of the value function. …”
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Preface by Azmy S. Ackleh, Linda J. S. Allen, Graciela Canziani, Shandelle M. Henson, Jia Li, Zhien Ma

“…In Athens, he became interested inecotoxicology and partial differential equation models ofphysiologically structured populations. …”
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Experimental Investigation and Analysis of Dynamic Buckling of Drill String in Horizontal Well by Fushen Ren, Baojin Wang, Lei Zhao, Anhe Zhu

“…This paper focuses on the rotational drill string in horizontal well. The differential equation of the dynamic buckling is established considering some various factors, including friction, the drill string-borehole interaction, and rotation, and the equations of the critical load of the sinusoidal buckling and the spiral buckling are derived. …”
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POSFUST RELIABILITY OF A NON-REPAIRABLE MULTI-STATE SYSTEM WITH POSFUST FAILURE RATE ESTIMATION by Harendra Yadav, Mukesh Kumar Sharma, Vishnu Narayan Mishra

“…In this approach, Markov process (multi-state system) is used for getting the governing differential equation for transition from one state to another state. …”
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Optimized Direct Padé and HPM for Solving Equation of Oxygen Diffusion in a Spherical Cell by M. A. Sandoval-Hernandez, H. Vazquez-Leal, A. Sarmiento-Reyes, U. Filobello-Nino, F. Castro-Gonzalez, A. L. Herrera-May, R. A. Callejas-Molina, R. Ruiz-Gomez

“…This work presents the application of homotopy perturbation method (HPM) and Optimized Direct Padé (ODP) to obtain a handy and easily computable approximate solution of the nonlinear differential equation to model the oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics. …”
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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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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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On the Stability of Eccentrically Compressed Reinforced Concrete Elements with a Small Eccentricity, Taking into Account the Rheological Properties of Concrete by A. G. Tamrazyan

“…Complicated integration is replaced by the solution of the differential equation of the bent axis of the rod in the form of a sinusoid half-wave.…”
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Response of Composite Beam Structure under Unbalanced Excitation of Rice Threshing System by Xujun Zhai, Xingqin You, Hao Zhang, Zhong Tang, Xinzhong Wang, Guoqiang Wang

“…This paper studies the dynamic response of the support beam under the unbalanced excitation of the rice threshing system. The differential equation of motion of the supporting beam under the action of harmonic force is established by the modal superposition method, and its dynamic response is analyzed. …”
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Pull-In and Snap-Through Analysis of Electrically Actuated Viscoelastic Curved Microbeam by Ehsan Akrami-Nia, Hamid Ekhteraei-Toussi

“…By applying the Galerkin method, the obtained governing equation is discretized, converted to a nonlinear differential equation, and solved by MATLAB software. Through a quasi-static analysis, the voltage and location of snap-through and pull-in instabilities are identified. …”
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