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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New Phase-Fitted and Amplification-Fitted Fourth-Order and Fifth-Order Runge-Kutta-Nyström Methods for Oscillatory Problems by K. W. Moo, N. Senu, F. Ismail, M. Suleiman

“…Two new Runge-Kutta-Nyström (RKN) methods are constructed for solving second-order differential equations with oscillatory solutions. These two new methods are constructed based on two existing RKN methods. …”
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Evolution-Operator-Based Single-Step Method for Image Processing

“…The key component of the proposed method is a local spectral evolution kernel (LSEK) that analytically integrates a class of evolution partial differential equations (PDEs). From the point of view PDEs, the LSEK provides the analytical solution in a single time step, and is of spectral accuracy, free of instability constraint. …”
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A Mathematical Model for DNA Damage and Repair by Philip S. Crooke, Fritz F. Parl

“…The model encompasses a set of differential equations representing the sequence of enzymatic reactions in both damage and repair pathways. …”
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On Fitting Of Mathematical Models Of Cell Signaling Pathways Using Adjoint Systems by Krzysztof Fujarewicz, Marek Kimmel, Andrzej Swierniak

“…Such models frequently take the form of a set ofnonlinear ordinary differential equations. While the model is continuous-time,the performance index, used in the fitting procedure, involves measurementstaken only at discrete-time moments. …”
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Time Delayed Stage-Structured Predator-Prey Model with Birth Pulse and Pest Control Tactics by Mei Yan, Yongfeng Li, Zhongyi Xiang

“…In order to better control the pests, two-time delayed stage-structured predator-prey models with birth pulse and pest control tactics are proposed and analyzed by using impulsive differential equations in present work. The stability threshold conditions for the mature prey-eradication periodic solutions of two models are derived, respectively. …”
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ANALYSIS OF THE INTERNAL RESONANCE CHARACTERISTICS OF RECTANGULAR CURRENT-CONDUCTING THIN PLATE IN TRANSVERSE MAGNETIC FIELD by LI Jing, HU YuDa

“…According to a rectangular plate with one side fixed and three other sides simply supported,time variable and space variable are separated by the displacement modal expansion and the method of Galerkin,and the two-degree-of-freedom internal resonance nonlinear vibration differential equations are obtained. By the method of multiple scales,the coupled characteristic equations of the first two order vibration modes are obtained under the case of 1∶3 internal resonance. …”
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Qualitative and Computational Analysis of a Mathematical Model for Tumor-Immune Interactions by F. A. Rihan, M. Safan, M. A. Abdeen, D. Abdel Rahman

“…We provide a family of ordinary and delay differential equations to model the dynamics of tumor-growth and immunotherapy interactions. …”
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A High Order Theory for Linear Thermoelastic Shells: Comparison with Classical Theories by V. V. Zozulya

“…Then in the same way as in the 3D theories system of differential equations in terms of displacements and boundary conditions for Fourier coefficients has been obtained. …”
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Representation of the solution of a nonlinear molecular beam epitaxy equation by Boubaker Smii

“…Stochastic partial differential equations (SPDEs) driven by Lévy noise are extensively employed across various domains such as physics, finance, and engineering to simulate systems experiencing random fluctuations. …”
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