Analysis of non scalar control problems for parabolic systems by the block moment method by Boyer, Franck, Morancey, Morgan

“…We also deduce estimates on the cost of controllability when the final time goes to the minimal null control time.We illustrate how the method works on a few examples of such abstract controlled systems and then we deal with actual coupled systems of one dimensional parabolic partial differential equations. Our strategy enables us to tackle controllability issues that seem out of reach by existing techniques.…”
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Electromagnetic Low-Frequency Dipolar Excitation of Two Metal Spheres in a Conductive Medium by Panayiotis Vafeas, Polycarpos K. Papadopoulos, Dominique Lesselier

“…The calculation of the exact solutions, satisfying Laplace’s and Poisson’s differential equations, leads to infinite linear systems, solved approximately within any order of accuracy through a cut-off procedure and via numerical implementation. …”
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Exploring the Inducement for Social Awareness Behavior and Optimal Control Strategy on Nipah Virus Transmission by Saima Efat, K. M. Ariful Kabir

“…We employ a system of nonlinear ordinary differential equations to dissect how the dynamics of primary infections impact the spread of Nipah disease. …”
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Solving Parabolic and Hyperbolic Equations with Variable Coefficients Using Space-Time Localized Radial Basis Function Collocation Method by Mohammed Hamaidi, Ahmed Naji, Ahmed Taik

“…The advantages of such formulation are (i) time discretization as implicit, explicit, θ-method, method-of-line approach, and others are not applied; (ii) the time stability analysis is not discussed; and (iii) recomputation of the resulting matrix at each time level as done for other methods for solving partial differential equations (PDEs) with variable coefficients is avoided and the matrix is computed once. …”
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Effect of Intervention of Vaccination and Treatment on the Transmission Dynamics of HBV Disease: A Mathematical Model Analysis by Firaol Asfaw Wodajo, Temesgen Tibebu Mekonnen

“…The model is studied qualitatively using the stability theory of differential equations and the effective reproductive number which represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. …”
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Motion Control of a 4WS4WD Path-Following Vehicle: Dynamics-Based Steering and Driving Models by Zhonghua Zhang, Caijin Yang, Weihua Zhang, Yanhai Xu, Yiqiang Peng, Maoru Chi

“…The vehicle path-following dynamics are modeled using the classical mass-damper-spring vibration theory, which is described by three ordinary differential equations of second order with lateral, heading and velocity deviations, and control parameters. …”
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The introduction of a rigid body of finite dimensions into an elastic-elastic half-space reinforced on the surface by a deformable plate by Kustarev G.V., Pavlov S.A., Rusinov K.A., Gusev A.A., Novotortsev N.V.

“…The integral differential equations determining the embedding of a rigid body of finite dimensions are solved using the discretization approach. …”
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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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A Multibody Model of Tilt-Rotor Aircraft Based on Kane’s Method by Jianmin Su, Chengyue Su, Sheng Xu, Xiaoxing Yang

“…The generalized active forces and generalized inertial forces of both the body and the nacelles (with rotors) are obtained, respectively, and the first-order differential equations of the generalized rates are obtained. …”
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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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Computational analysis of thermo-solutal Marangoni convective unsteady stagnation point flow of tetra hybrid nanofluid past rotating sphere with activation energy by Munawar Abbas, Hawzhen Fateh M. Ameen, Jihad Younis, Nargiza Kamolova, Ebenezer Bonyah, Hafiz Muhammad Ghazi

“…Using the proper similarity variables, ordinary differential equations (ODEs) are generated from the nonlinear governing equations. …”
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An integrated toolbox for creating neuromorphic edge applications by Lars Niedermeier, Nikil Dutt, Jeffrey L Krichmar

“…For instance, the mathematical foundation involves differential equations rather than basic activation functions. …”
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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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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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A quantitative analysis of Koopman operator methods for system identification and predictions by Zhang, Christophe, Zuazua, Enrique

“…It is based on the so-called Koopman operator, which uses the well-known link between differential equations and linear transport equations. Data-driven methods recover specific finite-dimensional approximations of the Koopman operator, which can be understood as a transport operator. …”
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How cells align to structured collagen fibrils: a hybrid cellular Potts and molecular dynamics model with dynamic mechanosensitive focal adhesions by Koen A. E. Keijzer, Erika Tsingos, Erika Tsingos, Roeland M. H. Merks, Roeland M. H. Merks

“…We present a hybrid computational model coupling three mathematical approaches: first, the cellular Potts model (CPM) describes an individual contractile cell; second, molecular dynamics (MD) represent the ECM as a network of cross-linked, deformable fibers; third, a set of ordinary differential equations (ODEs) describes the dynamics of the cell’s FAs, in terms of a balance between assembly and a mechanoresponsive disassembly. …”
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A Multiscale Fractal Approach for Determining Cushioning Curves of Low-Density Polymer Foams by Mariela C. Bravo-Sánchez, Luis M. Palacios-Pineda, José L. Gómez-Color, Oscar Martínez-Romero, Imperio A. Perales-Martínez, Daniel Olvera-Trejo, Jorge A. Estrada-Díaz, Alex Elías-Zúñiga

“…To capture the multiscale nature of the dynamic response behavior of two low-density foams to sustain impact loads, fractional differential equations of motion are used to qualitatively and quantitatively describe the dynamic response behavior, assuming restoring forces for each foam characterized, respectively, by a polynomial of heptic degree and by a trigonometric tangential function. …”
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Analyzing crop production: Unraveling the impact of pests and pesticides through a fractional model by Navnit Jha, Akash Yadav, Ritesh Pandey, A.K. Misra

“…The feasibility of every possible nonnegative equilibrium and its stability characteristics are explored utilizing the stability theory of fractional differential equations. Our model analysis reveals that in a continuous spray approach, the roles of pesticide abatement rate and pesticide uptake rate can be interchanged. …”
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On a New Epidemic Model with Asymptomatic and Dead-Infective Subpopulations with Feedback Controls Useful for Ebola Disease by M. De la Sen, A. Ibeas, S. Alonso-Quesada, R. Nistal

“…The global stability is formally discussed by using tools of qualitative theory of differential equations by using Gauss-Stokes and Bendixson theorems so that neither Lyapunov equation candidates nor the explicit solutions are used. …”
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