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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Global dynamics of a vector-host epidemic model with age of infection by Yan-Xia Dang, Zhi-Peng Qiu, Xue-Zhi Li, Maia Martcheva

“…In this paper, a partial differential equation (PDE) model is proposed to explore the transmission dynamics of vector-borne diseases. …”
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Application of Laplace Transform For Solving Population Growth and Decay Models. by Natukunda, Pamellah

“…Laplace can be used to convert complex differential equations to a simpler form having polynomials, convert derivatives into multiple domain variables, and then convert the polynomials back to the differential equation using the Inverse Laplace transform, telecommunication field to send signals to both sides of the medium. …”
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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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Research on Constriction Resistance of Drum Gear Coupling of High Speed EMU by Chunjun Chen, Xiang Zheng, Lu Yang, Linchun Zhou

“…Make use of the load distribution method to calculate the relationship between the load of each tooth and the total load of the coupling according to the flexural approximate differential equation of single tooth，according to the Hertz contact theory and the rough surface contact theory，the actual contact area and constriction resistance are calculated. …”
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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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