Mixed Convection in a Double Lid-Driven Wavy Shaped Cavity Filled with Nanofluid Subject to Magnetic Field and Internal Heat Source by Kakali Chowdhury, Md. Abdul Alim

“…The physical problems are characterized by 2D governing partial differential equations accompanying proper boundary conditions and are discretized using Galerkin’s finite element formulation. …”
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Mathematically modeling PCR: An asymptotic approximation with potential for optimization by Martha Garlick, James Powell, David Eyre, Thomas Robbins

“…A mathematical model for PCR (Polymerase Chain Reaction) is developed using the law of mass action and simplifying assumptions regarding the structure of the reactions. Differential equations are written from the chemical equations, preserving the detail of the complementary DNA single strand being extended one base pair at a time. …”
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Application of BSDE in Standard Inventory Financing Loan by Hui Zhang, Wenyu Meng, Xiaojie Wang, Jianwei Zhang

“…Applying backward stochastic differential equations (BSDEs), we get the explicit solutions of the models. …”
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A Novel Highly Nonlinear Quadratic System: Impulsive Stabilization, Complexity Analysis, and Circuit Designing by Arthanari Ramesh, Alireza Bahramian, Hayder Natiq, Karthikeyan Rajagopal, Sajad Jafari, Iqtadar Hussain

“…Most of the quadratic ordinary differential equations (ODEs) such as Chen, Rossler, and Lorenz have at least one linear term in their equations. …”
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Analytic-Numerical Solution of Random Boundary Value Heat Problems in a Semi-Infinite Bar by M.-C. Casabán, J.-C. Cortés, B. García-Mora, L. Jódar

“…Using previous results about random ordinary differential equations, a closed form solution stochastic process is firstly obtained. …”
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AI-assisted discovery of quantitative and formal models in social science by Julia Balla, Sihao Huang, Owen Dugan, Rumen Dangovski, Marin Soljačić

“…By extending neuro-symbolic methods to find compact functions and differential equations in noisy and longitudinal data, we show that our system can be used to discover interpretable models from real-world data in economics and sociology. …”
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Compartmental Models Driven by Renewal Processes: Survival Analysis and Applications to SVIS Epidemic Models by Divine Wanduku, Md Mahmud Hasan

“…The novel SVIS model is formulated as a non-autonomous nonlinear system (NANLS) of ordinary differential equations (ODEs), with coefficients defined by HRFs. …”
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Improved Riccati Transfer Matrix Method for Free Vibration of Non-Cylindrical Helical Springs Including Warping by A.M. Yu, Y. Hao

“…Free vibration equations for non-cylindrical (conical, barrel, and hyperboloidal types) helical springs with noncircular cross-sections, which consist of 14 first-order ordinary differential equations with variable coefficients, are theoretically derived using spatially curved beam theory. …”
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Application of Fuzzy Fractional Kinetic Equations to Modelling of the Acid Hydrolysis Reaction by Ferial Ghaemi, Robiah Yunus, Ali Ahmadian, Soheil Salahshour, Mohamed Suleiman, Shanti Faridah Saleh

“…The method is computationally interesting, and the numerical results demonstrate the effectiveness and validity of the method for solving fuzzy fractional differential equations.…”
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Vibration Characteristics for Moving Printing Membrane with Variable Density along the Lateral Direction by Mingyue Shao, Jimei Wu, Yan Wang, Qiumin Wu, Yuan Chen

“…The transverse vibration differential equations of moving membrane are established based on D’Alembert’s principle and discretized by using the differential quadrature method (DQM). …”
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Analysis of Nonlinear Structural Dynamics and Resonance in Trees by H. Doumiri Ganji, S.S. Ganji, D.D. Ganji, F. Vaseghi

“…Many of such nonlinear differential equations are complicated to solve. Therefore, this paper focuses on an accurate and simple solution, Differential Transformation Method (DTM), to solve the derived equation. …”
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Identification of a simplified mathematical model of an unmanned aerial vehicle by A. A. Lobaty, Y. F. Yatsyna, S. S. Prohorovith, Y. A. Hvitko

“…The analytical substantiation of the need to apply the methods of linearization of the mathematical model of UAV movement and the accepted assumptions for obtaining differential equations of UAV movement relative to the center of mass, allowing to synthesize the required transfer function of the corresponding element of the UAV control system. …”
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A Strongly A-Stable Time Integration Method for Solving the Nonlinear Reaction-Diffusion Equation by Wenyuan Liao

“…The semidiscrete ordinary differential equation (ODE) system resulting from compact higher-order finite difference spatial discretization of a nonlinear parabolic partial differential equation, for instance, the reaction-diffusion equation, is highly stiff. …”
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On Modeling and Constrained Model Predictive Control of Open Irrigation Canals by Lihui Cen, Ziqiang Wu, Xiaofang Chen, Yanggui Zou, Shaohui Zhang

“…As a set of hyperbolic partial differential equations, they are not solved explicitly and difficult to design optimal control algorithms. …”
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The Hadamard-PINN for PDE inverse problems: Convergence with distant initial guesses by Yohan Chandrasukmana, Helena Margaretha, Kie Van Ivanky Saputra

“…This paper presents the Hadamard-Physics-Informed Neural Network (H-PINN) for solving inverse problems in partial differential equations (PDEs), specifically the heat equation and the Korteweg–de Vries (KdV) equation. …”
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Differential Games of Rechargeable Wireless Sensor Networks against Malicious Programs Based on SILRD Propagation Model by Guiyun Liu, Baihao Peng, Xiaojing Zhong, Xuejing Lan

“…In this paper, nodes are divided into five states according to the residual energy and infection level, and the differential equations are constructed to describe the evolution of nodes. …”
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Resolvent Positive Operators and Positive Fractional Resolvent Families by Nan-Ding Li, Ru Liu, Miao Li

“…Some examples of positive solutions to fractional differential equations are presented to illustrate our results.…”
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The Quantum Analysis of Nonlinear Optical Parametric Processes with Thermal Reservoirs by Tamirat Abebe, Nebiyu Gemechu, Chimdessa Gashu, Kebede Shogile, Solomon Hailemariam, Shimelis Adisu

“…In this paper, employing the stochastic differential equations associated with the normal ordering, the quantum properties of a nondegenerate three-level cascade laser with a parametric amplifier and coupled to a two-mode thermal reservoir are thoroughly analyzed. …”
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Dynamic Response of Parallel Hoisting System under Drive Deviation between Ropes with Time-Varying Length by Guohua Cao, Xiang Cai, Naige Wang, Weihong Peng, Jishun Li

“…The slack situation of the rope is considered, and the dynamic equations which are systems of DAEs are transformed to ordinary differential equations (ODEs). The dynamic responses of tension, torsion, and acceleration are analyzed considering radius’ error of the drums, which indicates that the drive deviation between ropes can cause large influence on the tension difference and even cause one of the ropes to slack. …”
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Models for the spread and persistence of hantavirus infection in rodents with direct and indirect transmission by Curtis L. Wesley, Linda J. S. Allen, Michel Langlais

“…Two models are analyzed, a nonautonomous system of differential equations with time-periodic coefficients and an autonomous system, where the coefficients are taken to be the time-average. …”
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