Optimal System, Reductions, and Conservation Laws of a Nonlinear Damped Klein-Gordon- Fock Equation by Faiza Arif, F. M. Mahomed, F. D. Zaman, M. T. Mustafa

“…Using the similarity transformation method, the above-mentioned partial differential equation is reduced into a set of ordinary differential equations. …”
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Advanced neural network modeling with Levenberg–Marquardt algorithm for optimizing tri-hybrid nanofluid dynamics in solar HVAC systems by A. Aziz, S.A.H. Shah, H.M.S. Bahaidarah, T. Zamir, T. Aziz

“…The nonlinear differential equations derived from the physical model are solved using the three-step Lobatto IIIa method, ensuring precision and reliability. …”
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The g-generalized Mittag-Leffler (p,s,k)-function by Umbreen Ayub, Madiha Shafiq, Amir Abbas, Umair Khan, Anuar Ishak, Y.S. Hamed, Homan Emadifar

“…It may be used to solve a variety of fractional differential equations (FDEs) including fractional Laplace and fractional Poisson equations. …”
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Accelerated pseudo-transient method for elastic, viscoelastic, and coupled hydromechanical problems with applications by Y. Alkhimenkov, Y. Y. Podladchikov

“…<p>The accelerated pseudo-transient (APT) method is a matrix-free approach used to solve partial differential equations (PDEs), characterized by its reliance on local operations, which makes it highly suitable for parallelization. …”
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Method for Calculating Transients in a Gas Pipeline by A. S. Fikov

“…An analytical solution of a system of partial differential equations describing the unsteady isothermal flow of real gases in gas pipelines is considered. …”
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Role of white-tailed deer in geographic spread of the black-legged tick Ixodes scapularis : Analysis of a spatially nonlocal model by Stephen A. Gourley, Xiulan Lai, Junping Shi, Wendi Wang, Yanyu Xiao, Xingfu Zou

“…The model turns out to be a system of differential equations with a spatially non-local term accounting for the phenomenon that a questing female adult tick that attaches to a deer at one location may later drop to the ground, fully fed, at another location having been transported by the deer. …”
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Formation of unmanned aircraft trajectory when flying around prohibited areas by A. A. Lobaty, A. Y. Bumai, A. M. Avsievich

“…A mathematical model of UAV motion in the horizontal plane is proposed, in the form of a system of ordinary differential equations in the Cauchy form. A law for measuring the control acceleration of the UAV’s center of mass is obtained on the basis of specifying the minimized quality functional and the corresponding constraints, which is a feature of the considered method of solving the problem. …”
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<i>DynPy</i>—Python Library for Mechanical and Electrical Engineering: An Assessment with Coupled Electro-Mechanical Direct Current Motor Model by Damian Sierociński, Bogumił Chiliński, Franciszek Gawiński, Amadeusz Radomski, Piotr Przybyłowicz

“…In the paper examples for obtaining analytical and numerical solutions of the systems described with ordinary differential equations were presented. The assessment of solver accuracy was conducted utilising a coupled electro-mechanical model of a direct current motor, with <i>MATLAB/Simulink</i> (R2022b) used as a reference tool. …”
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Micromechanics of Cracked Laminates under Uniaxial Load: A Comparison between Approaches by J. A. Rivera-Santana, A. Guevara-Morales, U. Figueroa-López

“…All of these include the process of defining 0/90s laminate unit cell, from which governing differential equations and corresponding boundary conditions are stated. …”
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Investigating nonlinear dynamic properties of an inertial sensor with rotational velocity-dependent rigidity by Mina Ghanbari, Mohammad Fathalilou, Hamed Haddad Khodaparast, Ghader Rezazadeh

“…The numerical Galerkin approach is employed for discretization of the coupled differential equations in spatial coordinates. To obtain the sensor response as a function of frequency, a continuation arc-length method based on weak formulation energy balance method is used. …”
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Intelligent back-propagated neural networks to study nonlinear heat transfer in tangent-hyperbolic fluids by Muhammad Asif Zahoor Raja, Huma Tayyab, Aamna Muskan Malik, Qazi Mahmood Ul Hassan, Kottakkaran Sooppy Nisar, Muhammad Shoaib

“…The controlling PDEs are similarly converted into nonlinear ordinary differential equations (ODEs), and reference data is generated using the Adam-Bashforth numerical solver. …”
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An Updating Method for Finite Element Models of Flexible-Link Mechanisms Based on an Equivalent Rigid-Link System by R. Belotti, R. Caracciolo, I. Palomba, D. Richiedei, A. Trevisani

“…This paper proposes a comprehensive methodology to update dynamic models of flexible-link mechanisms (FLMs) modeled through ordinary differential equations. The aim is to correct mass, stiffness, and damping matrices of dynamic models, usually based on nominal and uncertain parameters, to accurately represent the main vibrational modes within the bandwidth of interest. …”
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Nonlinear Dynamic Response Analysis of Cable–Buoy Structure Under Marine Environment by Qiufu Xie, Binghan Liu, Junxian Zhang, Yaobing Zhao

“…To address these challenges, this study derives coupled differential equations for the cable–buoy structure based on the two drag force models. …”
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Exploring the solutions of tempered (κ,ϖ)-Hilfer hybrid implicit boundary value problem by Abdelkrim Salim, Sabri T.M. Thabet, Ava Sh. Rafeeq, Mohammad Esmael Samei, Imed Kedim, Miguel Vivas-Cortez

“…Our study leverages the properties of tempered (κ,ϖ)-Hilfer fractional operators to explore the mathematical underpinnings of the problem, which is characterized by implicit nonlinear fractional differential equations. To derive the results, we employ Banach’s fixed point theorem, which facilitates the demonstration of the existence of solutions under certain contractive conditions. …”
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A Fluid Model for Mobile Data Offloading Based on Device-to-Device Communications with Time Constraints by Antonio Pinizzotto, Raffaele Bruno

“…To address this issue, we propose a novel fluid model based on ordinary differential equations (ODEs) for the performance analysis of a general D2D-based mobile data offloading scheme, called OORS, which considers both content delivery guarantees and time limitations for storing content copies in local device caches, making it more practical for real-world applications. …”
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Effect of Rising Temperature on Lyme Disease: Ixodes scapularis Population Dynamics and Borrelia burgdorferi Transmission and Prevalence by Dorothy Wallace, Vardayani Ratti, Anita Kodali, Jonathan M. Winter, Matthew P. Ayres, Jonathan W. Chipman, Carissa F. Aoki, Erich C. Osterberg, Clara Silvanic, Trevor F. Partridge, Mariana J. Webb

“…A temperature-driven seasonal model of Borrelia burgdorferi (Lyme disease) transmission among four host types is constructed as a system of nonlinear ordinary differential equations. The model is developed and parametrized based on a collection of lab and field studies. …”
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Optimal control strategies for toxoplasmosis disease transmission dynamics via harmonic mean-type incident rate by Usman Khan, Farhad Ali, Ohud A. Alqasem, Maysaa E. A. Elwahab, Ilyas Khan, Ariana Abdul Rahimzai

“…The disease dynamics are first schematically illustrated, and then the law of mass action is applied to obtain nonlinear ordinary differential equations (ODEs). Analysis of the boundedness, positivity, and equilibrium points of the system has been analyzed. …”
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DyCeModel: a tool for 1D simulation for distribution of plant hormones controlling tissue patterning by D. S. Azarova, N. A. Omelyanchuk, V. V. Mironova, E. V. Zemlyanskaya, V. V. Lavrekha

“…Here, we present DyCeModel, a software tool implemented in MATLAB for one-dimensional simulation of tissue with a dynamic cellular ensemble, where changes in hormone (or other active substance) concentration in the cells are described by ordinary differential equations (ODEs). We applied DyCeModel to simulate cell dynamics in plant meristems with different cellular structures and demonstrated that DyCeModel helps to identify the relationships between hormone concentration and cellular behaviors. …”
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How Do Diabetes Models Measure Up? A Review of Diabetes Economic Models and ADA Guidelines by Lindsay Govan, Olivia Wu, Robert Lindsay, Andrew Briggs

“…There are four main types of models: Markov-based cohort, Markov-based microsimulations, discrete-time microsimulations, and continuous time differential equations. All models were long-term diabetes models incorporating a wide range of compilations from various organ systems. …”
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Dynamic analysis and comparison of the performance of linear and nonlinear controllers applied to a nonlinear non-interactive and interactive process by José M. Campos-Salazar, Pablo Lecaros, Rodrigo Sandoval-García

“…The process dynamics were initially modeled using nonlinear differential equations, which were subsequently linearized to facilitate the design of the PI and LQR controllers. …”
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