A Four-Zone Model and Nonlinear Dynamic Analysis of Solution Multiplicity of Buoyancy Ventilation in Underground Building by Yuxing Wang, Chunyu Wei

“…The underground structure is divided to four zones, a differential equation is established in each zone, and therefore, there are four differential equations in the underground structure. …”
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A Finite Difference Method for Solving Unsteady Fractional Oldroyd-B Viscoelastic Flow Based on Caputo Derivative by Fang Wang, Yu Wang

“…In order to improve the degree of accuracy, the mixed partial derivative including the fractional derivative in the differential equation is converted effectively by integrating by parts instead of by direct discretization. …”
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Numerical Solutions of Micropolar Nanofluid over an Inclined Surface Using Keller Box Analysis by Khuram Rafique, Hammad Alotaibi, Taher A. Nofal, Muhammad Imran Anwar, Masnita Misiran, Ilyas Khan

“…Compatible transformations are implemented to attain the nonlinear differential equation from the boundary value PDE’s. The physical quantities of practical interest are treated by graphically as well as numerically. …”
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Richards equation for the assessment of landslide hazards by Ramesh Chandra Timsina

“…However, as a highly nonlinear parabolic partial differential equation (PDE), it has limited analytic solutions, which often lack precision in practical scenarios. …”
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Supercritical Nonlinear Vibration of a Fluid-Conveying Pipe Subjected to a Strong External Excitation by Yan-Lei Zhang, Hui-Rong Feng, Li-Qun Chen

“…The motion measured from each of curved equilibrium configurations is governed by a nonlinear integro-partial-differential equation with variable coefficients. The Galerkin method is employed to discretize the governing equation into a gyroscopic system consisting of a set of coupled nonlinear ordinary differential equations. …”
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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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Simulation and Domain Identification of Sea Ice Thermodynamic System by Bing Tan, Peng Lu, Zhijun Li, Enmin Feng, Juan Wang

“…Based on the measured data and characteristics of sea ice temperature distribution in space and time, this study is intended to consider a parabolic partial differential equation of the thermodynamic field of sea ice (coupled by snow, ice, and sea water layers) with a time-dependent domain and its parameter identification problem. …”
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Comparative Studies of Nonlinear Models and Their Applications to Magmatic Evolution and Crustal Growth of the Huai’an Terrane in the North China Craton by Qiuming Cheng, Min Gao

“…This paper introduces these nonlinear functions derived from a unified differential equation, with parameters that reflect their relative nonlinearities and singularities, enabling their comparative application. …”
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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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Vibration of a Cylindrical Tunnel under a Centric Point-Source Explosion by Yuetang Zhao, Cheng Chu, Anastasios Vafeidis, Jie Li

“…The governing equation of the motion is a fourth-order partial differential equation, for which a numerical method combining finite difference with the implicit Newmark-β method was adopted. …”
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Deterministic and Stochastic Study for an Infected Computer Network Model Powered by a System of Antivirus Programs by Youness El Ansari, Ali El Myr, Lahcen Omari

“…Furthermore, we use the Itô formula and some other theoretical theorems of stochastic differential equation to discuss the extinction and the stationary distribution of our system. …”
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Analysis of Bianchi Type V Holographic Dark Energy Models in General Relativity and Lyra’s Geometry by Daba Meshesha Gusu, M. Vijaya Santhi

“…The solutions of differential equation fields have been obtained by considering two specific cases, namely, the expansion scalar θ in the model is proportional to the shear scalar σ and the average scale factor taken as hybrid expansion form. …”
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Numerical Solutions of Duffing Van der Pol Equations on the Basis of Hybrid Functions by M. Mohammadi, A. R. Vahidi, T. Damercheli, S. Khezerloo

“…The next technique is to convert this equation into a system of ordinary differential equation of the first order (SODE) and solve it according to the proposed approximate method. …”
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Quantization of a 3D Nonstationary Harmonic plus an Inverse Harmonic Potential System by Salim Medjber, Hacene Bekkar, Salah Menouar, Jeong Ryeol Choi

“…In particular, the Nikiforov-Uvarov method with an appropriate coordinate transformation enabled us to reduce the eigenvalue equation of the invariant operator, which is a second-order differential equation, to a hypergeometric-type equation that is convenient to treat. …”
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A Pest Management Model with Stage Structure and Impulsive State Feedback Control by Guoping Pang, Zhiqing Liang, Weijian Xu, Lijie Li, Gang Fu

“…We get the sufficient condition for the existence of the order-1 periodic solution by differential equation geometry theory and successor function. …”
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Trivariate Stochastic Weather Model for Predicting Maize Yield by Patrick Chidzalo, Phillip O. Ngare, Joseph K. Mung’atu

“…Stochastic analyses are applied on the pdf and process to account for nonlinearity and nonstationarity, and also establish a corresponding stochastic differential equation (SDE) for maize yield. The trivariate stochastic process predicts maize yield with R2=0.8389 and MAPE=4.31% under a deep learning framework. …”
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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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Complex dynamics of a predator-prey fishery model: The impact of the Allee effect and bilateral intervention by Yuan Tian, Yang Liu, Kaibiao Sun

“…The existence and stability of the order-1 periodic solution and the order-2 periodic solution of the control system are analyzed by using the differential equation geometry theory. Additionally, numerical simulations are carried out to verify the correctness of the conclusions, and illustrate the impact of the Allee effect and bilateral intervention on the ecosystem, which provides an effective method for modern fishery conservation and harvesting.…”
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A Spatial Euler-Bernoulli Beam Element for Rigid-Flexible Coupling Dynamic Analysis of Flexible Structures by Zhigang Zhang, Zhaohui Qi, Zhigang Wu, Huiqing Fang

“…Thus all the high frequencies can be filtered out and a corresponding equivalent internal damping will be produced in this new formulation, which can improve the computation performance of the proposed element for solving the stiff problem and evaluate the governing equations even by using the nonstiff ordinary differential equation solver. Finally, several numerical examples are carried out to verify the validation and efficiency of this proposed formulation by comparison with the analytical solutions and other research works.…”
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