NONLINEAR VIBRATION RESEARCH OF STRIP STEEL WITH CONSIDERATION OF TORSIONAL VIBRATION OF MAIN DRIVE SYSTEM OF ROLLING MILL by GAO ChongYi, DU GuoJun, LI Rui, LIU XiaoMan

“…Then, the nonlinear vibration differential equations of the coupled model were derived with Hamilton’s principle. …”
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A structured model for the spread of Mycobacterium marinum: Foundations for a numerical approximation scheme by Azmy S. Ackleh, Mark L. Delcambre, Karyn L. Sutton, Don G. Ennis

“…The model consists of a system of nonlinear hyperbolic partial differential equations coupled with three nonlinear ordinary differential equations. …”
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Optimal Portfolio Selection of Mean-Variance Utility with Stochastic Interest Rate by Shuang Li, Shican Liu, Yanli Zhou, Yonghong Wu, Xiangyu Ge

“…By solving the corresponding nonlinear partial differential equations (PDEs) deduced from the extended HJB equation, the analytical solutions of the optimal investment strategies under time inconsistency are derived. …”
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Sliding Mode Output Feedback Control of a Flexible Rotor Supported by Magnetic Bearings by A. S. Lewis, A. Sinha, K. W. Wang

“…A mathematical model of the rotor]magnetic bearing system is presented in terms of partial differential equations. These equations are then discretized into a finite number of ordinary differential equations through Galerkin’s method. …”
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Global Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and Latency by Rodrigue Yves M’pika Massoukou, Suares Clovis Oukouomi Noutchie, Richard Guiem

“…The model is a coupled system of (hyperbolic) partial differential equations with ordinary differential equations. …”
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Chemical Reaction and Generalized Heat Flux Model for Powell–Eyring Model with Radiation Effects by Faisal Salah

“…This contrast is important because it shows how precisely the successive linearization method can resolve a set of nonlinear differential equations. Following that, the generated solution is studied and explained in relation to a variety of engineering parameters. …”
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DC Glow Discharge in Axial Magnetic Field at Low Pressures by Shen Gao, Shixiu Chen, Zengchao Ji, Wei Tian, Jun Chen

“…Results obtained from the model reveal that although the differential equations under the condition of axial magnetic field are consistent with the differential equations without considering the magnetic field, the solution of the equations is not completely consistent. …”
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Combined Effect of Buoyancy Force and Navier Slip on MHD Flow of a Nanofluid over a Convectively Heated Vertical Porous Plate by Winifred Nduku Mutuku-Njane, Oluwole Daniel Makinde

“…A suitable similarity transformation is employed to reduce the governing partial differential equations into nonlinear ordinary differential equations, which are solved numerically by employing fourth-order Runge-Kutta with a shooting technique. …”
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Solving Nonlinear Energy Supply and Demand System Using Physics-Informed Neural Networks by Van Truong Vo, Samad Noeiaghdam, Denis Sidorov, Aliona Dreglea, Liguo Wang

“…Nonlinear differential equations and systems play a crucial role in modeling systems where time-dependent factors exhibit nonlinear characteristics. …”
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Mathematical modelling of MHD hybrid nanofluid flow in a convergent and divergent channel under variable thermal conductivity effect by Alharbi Abdulaziz H.

“…H2O{\text{H}}_{\text{2}}\text{O}) are considered in this work. The partial differential equations modelling the problem are reduced to ordinary differential equations following the application of the similarity transformations. …”
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Analysis of Heat Transfer in Berman Flow of Nanofluids with Navier Slip, Viscous Dissipation, and Convective Cooling by O. D. Makinde, S. Khamis, M. S. Tshehla, O. Franks

“…The governing partial differential equations and boundary conditions are converted into a set of nonlinear ordinary differential equations using appropriate similarity transformations. …”
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A computational scheme of exponential integrator for fuzzy electrical boundary layer flow with variable viscosity and thermal conductivity by Muhammad Shoaib Arif, Kamaleldin Abodayeh, Yasir Nawaz

“…This study aims to d an efficient computational scheme for solving partial differential equations involving fuzzy parameters in boundary layer flow. …”
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Analytic Approximate Solutions for MHD Boundary-Layer Viscoelastic Fluid Flow over Continuously Moving Stretching Surface by Homotopy Analysis Method with Two Auxiliary Parameters by M. M. Rashidi, E. Momoniat, B. Rostami

“…The nonlinear ordinary differential equations for the momentum and energy equations are obtained and solved analytically by using homotopy analysis method (HAM) with two auxiliary parameters for two classes of visco-elastic fluid (Walters’ liquid B and second-grade fluid). …”
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Positivity of Fundamental Matrix and Exponential Stability of Delay Differential System by Alexander Domoshnitsky, Roman Shklyar, Mikhail Gitman, Valery Stolbov

“…Results on nonnegativity of the Cauchy matrix for system of delay differential equations xi′t+∑j=1n‍pijtxjhijt=fit,   i=1,…,n, which were based on nonpositivity of all diagonal elements, were presented in the previous works. …”
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MHD Natural Convection with Convective Surface Boundary Condition over a Flat Plate by Mohammad M. Rashidi, Mohammad Ferdows, Amir Basiri Parsa, Shirley Abelman

“…Numerical solutions of the ordinary differential equations are obtained by the Keller Box method for different values of the controlling parameters associated with the problem.…”
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Global Well-Posedness and Determining Nodes of Non-Autonomous Navier–Stokes Equations with Infinite Delay on Bounded Domains by Huanzhi Ge, Feng Du

“…The asymptotic behavior of solutions to nonlinear partial differential equations is an important tool for studying their long-term behavior. …”
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Principal Component Analysis in the Nonlinear Dynamics of Beams: Purification of the Signal from Noise Induced by the Nonlinearity of Beam Vibrations by A. V. Krysko, Jan Awrejcewicz, Irina V. Papkova, Olga Szymanowska, V. A. Krysko

“…Solutions to linear and nonlinear differential equations are found using the principal component analysis (PCA).…”
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Dynamical Models of Tuberculosis and Their Applications by Carlos Castillo-Chavez, Baojun Song

“…Modelformulations involve a variety of mathematical areas, such as ODEs(Ordinary Differential Equations) (both autonomous andnon-autonomous systems), PDEs (Partial Differential Equations),system of difference equations, system of integro-differentialequations, Markov chain model, and simulation models.…”
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A Mathematical Model for a Transmissible Disease with a Variant by A. Otto, M. Amidou

“…The model is studied using the stability theory for systems of differential equations and the basic reproduction number R0. …”
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Double-Diffusive MHD Viscous Fluid Flow in a Porous Medium in the Presence of Cattaneo-Christov Theories by Bidemi Olumide Falodun, Adeola John Omowaye, Funmilayo Helen Oyelami, Homan Emadifar, Ahmed A. Hamoud, S. M. Atif

“…A set of partial differential equations governs the current design (PDEs). …”
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