Mathematical Modeling of Wax Deposition in Field-Scale Crude Oil Pipeline Systems by Francis Oketch Ochieng, Mathew Ngugi Kinyanjui, Jeconia Okelo Abonyo, Phineas Roy Kiogora

“…The coupled nonlinear partial differential equations governing the flow are discretized in time by a second-order semi-implicit time discretization scheme based on the Adams-Bashforth and Crank-Nicolson methods, which completely decouples the computation of the governing equations. …”
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Asymptotic analysis of mathematical model describing a new treatment of breast cancer using AZD9496 and palbociclib by Ophir Nave, Ophir Nave

“…The mathematical model that described the interaction between the cancer cells, the treatment, and the immune system cells includes a system of nonlinear ordinary differential equations of the firs order. In general, dynamic variables of a given system change each at a different rate. …”
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Physics-Informed Neural Network for modeling and predicting temperature fluctuations in proton exchange membrane electrolysis by Islam Zerrougui, Zhongliang Li, Daniel Hissel

“…This method solves differential equations and estimates the unknown parameters governing the temperature dynamics within the PEM electrolysis system. …”
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Mathematical Modelling of Cholera Transmission incorporating Media Coverage. by Muhereza, Obed

“…The model was thereafter analyzed using the stability theory of differential equations. The basic reproduction number Ra, was derived using the next generation matrix approach. …”
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Modeling Highly Buoyant Flows in the Castel Giorgio: Torre Alfina Deep Geothermal Reservoir by Giorgio Volpi, Fabien Magri, Francesca Colucci, Thomas Fisher, Mattia De Caro, Giovanni B. Crosta

“…The open source finite-element code OpenGeoSys is applied to solve the coupled systems of partial differential equations. The commercial software FEFLOW® is also used as additional numerical constraint. …”
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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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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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Computational analysis for efficient thermal transportation of ternary hybrid nanofluid flow across a stretching sheet with Cattaneo-Christov heat flux model by Wei Li, Shan Ali Khan, Muhammad Shafqat, Qamar Abbas, Taseer Muhammad, Muhammad Imran

“…The phenomenon were designed as partial differential equations. These are condensed to system of ODEs via similarity transformations. …”
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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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A computational role of blood nanofluid induced by a stenosed artery with porous medium and thermophoretic particle deposition effects by Shivalila Hangaragi, N. Neelima, N. Beemkumar, Ankur Kulshreshta, Umair Khan, Noreen Sher Akbar, Mohammad Kanan, Mona Mahmoud

“…Based on these assumptions, the governing equations are formulated and transformed into a system of ordinary differential equations using appropriate similarity transformations. …”
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Mixed Convective-Radiative Dissipative Magnetized Micropolar Nanofluid Flow over a Stretching Surface in Porous Media with Double Stratification and Chemical Reaction Effects: ADM-... by P. K. Pattnaik, M. M. Bhatti, S. R. Mishra, Munawwar Ali Abbas, O. Anwar Bég

“…The nonlinear governing partial differential conservation equations are rendered into nonlinear ordinary differential equations via relevant transformations. An innovative semi-numerical methodology combining the Adomian decomposition method (ADM) with Padé approximants and known as ADM-Padé is deployed to solve the emerging nonlinear ordinary differential boundary value problem with appropriate wall and free stream conditions in MATLAB software. …”
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On the transitory performance of mixed convective heat and mass transfer around spherical region in the presence of fluctuating streams by Hossam A. Nabwey, Sahar Anwar, Muhammad Ashraf, A.M. Rashad

“…For this purpose, the coupled partial differential equations are first non-dimensionalized and their steady and oscillatory components are separated. …”
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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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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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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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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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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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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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A ternary hybrid model for analysis of enhanced heat transport in non-Newtonian nanofluid over cylindrical geometry with effect of infinite shear rate viscosity by Hakim AL Garalleh

“…Based on assumptions of current study, the governing partial differential equations (PDEs) are formed and then transformed into ODEs for numerical solution. …”
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