Modeling of the migration of endothelial cells on bioactive micropatterned polymers by Thierry Colin, Marie-Christine Durrieu, Julie Joie, Yifeng Lei, Youcef Mammeri, Clair Poignard, Olivier Saut

“…It isbased on a system of partial differential equations ofPatlak-Keller-Segel type that describes theevolution of the cell densities. …”
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Control Application of Piezoelectric Materials to Aeroelastic Self-Excited Vibrations by Mohammad Amin Rashidifar, Darvish Ahmadi

“…The governing differential equations of an overhung beam are established. …”
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A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems by S. S. Motsa

“…The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. …”
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A One-Point Third-Derivative Hybrid Multistep Technique for Solving Second-Order Oscillatory and Periodic Problems by Mufutau Ajani Rufai, Ali Shokri, Ezekiel Olaoluwa Omole

“…This paper describes a third-derivative hybrid multistep technique (TDHMT) for solving second-order initial-value problems (IVPs) with oscillatory and periodic problems in ordinary differential equations (ODEs), the coefficients of which are independent of the frequency omega and step size h. …”
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Peridynamic Formulation for Coupled Thermoelectric Phenomena by Migbar Assefa, Xin Lai, Lisheng Liu, Yang Liao

“…This is because traditional methods are developed based on partial differential equations (PDEs) and lead to infinite fluxes at the discontinuities. …”
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Effects of Thermal Radiation on Mixed Convection Flow of a Micropolar Fluid from an Unsteady Stretching Surface with Viscous Dissipation and Heat Generation/Absorption by Khilap Singh, Manoj Kumar

“…The model contains nonlinear coupled partial differential equations which have been converted into ordinary differential equation by using the similarity transformations. …”
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Some Properties of Solutions to Multiterm Fractional Boundary Value Problems with p-Laplacian Operator by KumSong Jong, HuiChol Choi, KyongJun Jang, SongGuk Jong, KyongSon Jon, Ok Ri

“…In this paper, we study some properties of positive solutions to a class of multipoint boundary value problems for nonlinear multiterm fractional differential equations with p-Laplacian operator. Using the Banach contraction mapping principle, the existence, the uniqueness, the positivity, and the continuous dependency on m-point boundary conditions of the solutions to the given problem are investigated. …”
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Finite element approximation of a population spatial adaptation model by Gonzalo Galiano, Julián Velasco

“…In [18], Sighesada, Kawasaki and Teramoto presented a system of partial differential equations for modeling spatial segregation of interacting species. …”
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Robust H∞ Control for a Class of Nonlinear Distributed Parameter Systems via Proportional-Spatial Derivative Control Approach by Cheng-Dong Yang, Jianlong Qiu, Jun-Wei Wang

“…This paper addresses the problem of robust H∞ control design via the proportional-spatial derivative (P-sD) control approach for a class of nonlinear distributed parameter systems modeled by semilinear parabolic partial differential equations (PDEs). By using the Lyapunov direct method and the technique of integration by parts, a simple linear matrix inequality (LMI) based design method of the robust H∞ P-sD controller is developed such that the closed-loop PDE system is exponentially stable with a given decay rate and a prescribed H∞ performance of disturbance attenuation. …”
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Modeling colony collapse disorder in honeybees as a contagion by Christopher M. Kribs-Zaleta, Christopher Mitchell

“…The system of three ordinary differential equations accounts for multiple hive population behaviors including Allee effects and colony collapse. …”
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Importance of Activation Energy on Magnetized Dissipative Casson-Maxwell Fluid through Porous Medium Incorporating Chemical Reaction, Joule Heating, and Soret Effects: Numerical St... by Nesreen Althobaiti

“…The method transforms partial differential equations originating in fluidic systems into nonlinear differential equation systems with the proper degree of similarity which is subsequently resolved utilizing the Lobatto IIIA technique’s powerful computing capabilities. …”
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Modeling the Effects of Nonpharmaceutical Interventions on COVID-19 Spread in Kenya by Duncan K. Gathungu, Viona N. Ojiambo, Mark E. M. Kimathi, Samuel M. Mwalili

“…The resulting system of ordinary differential equations (ODEs) is solved using fourth-order and fifth-order Runge–Kutta methods. …”
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Douglas' Factorization Theorem and Atomic System in Hilbert Pro-$C^{\ast}$-Modules by Mohamed Rossafi, Roumaissae Eljazzar, Ram Mohapatra

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DYNAMIC MODEL OF THE BUDGET OF AN EDUCATIONAL INSTITUTION by Antonina V. Ganicheva, Aleksey V. Ganichev

“…Methodology: modeling, theory of solving differential equations. Results: a modified Keynes model has been developed, allowing for the calculation and optimization of the budget of educational organizations. …”
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A Simple Mathematical Model of Cyclic Circadian Learning by J. Šimon, M. Bulko

“…By the use of these functions and by formalism of differential equations, the concurrent processes of learning and forgetting are described mathematically. …”
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Analysis of electroelastic frictionless contact problems with adhesion by Mircea Sofonea, Rachid Arhab, Raafat Tarraf

“…The proofs are based on arguments of time-dependent variational inequalities, differential equations, and fixed point. Moreover, we prove that the solution of the Signorini contact problem can be obtained as the limit of the solution of the contact problem with normal compliance as the stiffness coefficient of the foundation converges to infinity.…”
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Viscous Flow over Nonlinearly Stretching Sheet with Effects of Viscous Dissipation by Javad Alinejad, Sina Samarbakhsh

“…The similarity transformation reduces the time-independent boundary layer equations for momentum and thermal energy into a set of coupled ordinary differential equations. The obtained equations, including nonlinear equation for the velocity field 𝑓 and differential equation by variable coefficient for the temperature field 𝜃, are solved numerically by using the fourth order of Runge-Kutta integration scheme accompanied by shooting technique with Newton-Raphson iteration method. …”
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Leveraging dynamics informed neural networks for predictive modeling of COVID-19 spread: a hybrid SEIRV-DNNs approach by Cheng Cheng, Elayaraja Aruchunan, Muhamad Hifzhudin Noor Aziz

“…This work integrates differential equations with deep neural networks to predict time-varying parameters in the SEIRV model. …”
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Analysis and Enhancements of a Prolific Macroscopic Model of Epilepsy by Christopher Fietkiewicz, Kenneth A. Loparo

“…Specifically, we analyze three aspects of the models: (1) Using dynamical systems analysis, we demonstrate and explain the presence of direct current potentials in the simulated EEG that were previously undocumented. (2) We explain how the system was not ideally formulated for numerical integration of stochastic differential equations. A reformulated system is developed to support proper methodology. (3) We explain an unreported contradiction in the published model specification regarding the use of a mathematical reduction method. …”
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Improvement of Image Compression by Changing the Mathematical Equation Style in Communication Systems by Riyadh M. Al-Saleem, Yasameen A. Ghani, Shihab A. Shawkat

“…The test images for these patterns showed a discrepancy in the image resolution when the compression coefficient was increased, as the results using three types of image compression methods proved a clear superiority when using “partial differential equations (PDE)”.…”
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