A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams by Nicholas H. Erdelyi, Seyed M. Hashemi

“…Using the Euler-Bernoulli bending beam theory, the governing differential equations are exploited and representative, frequency-dependent, field variables are chosen based on the closed form solution to these equations. …”
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The global stability of an SIRS model with infection age by Yuming Chen, Junyuan Yang, Fengqin Zhang

“…In this paper, we consider an SIRS modelwith infection age, which is described by a mixed system ofordinary differential equations and partial differentialequations. …”
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Graph-theoretic conditions for zero-eigenvalue Turing instability in general chemical reaction networks by Maya Mincheva, Gheorghe Craciun

“…If the SR graph satisfies certain conditions, similar to the conditions for ruling out multiple equilibria in spatially homogeneous differential equations systems, then the corresponding mass-action reaction-diffusion system cannot exhibit zero-eigenvalue Turing instability for any parameter values.On the other hand, if the graph-theoretic condition for ruling out zero-eigenvalue Turing instability is not satisfied, then the corresponding model may display zero-eigenvalue Turing instability for some parameter values. …”
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The Hadamard-PINN for PDE inverse problems: Convergence with distant initial guesses by Yohan Chandrasukmana, Helena Margaretha, Kie Van Ivanky Saputra

“…This paper presents the Hadamard-Physics-Informed Neural Network (H-PINN) for solving inverse problems in partial differential equations (PDEs), specifically the heat equation and the Korteweg–de Vries (KdV) equation. …”
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Studies on the Effects of Interphase Heat Exchange during Thermal Explosion in a Combustible Dusty Gas with General Arrhenius Reaction-Rate Laws by K. S. Adegbie, F. I. Alao

“…The equations governing the physical model with realistic assumptions are stated and nondimensionalised leading to an intractable system of first-order coupled nonlinear differential equations, which is not amenable to exact methods of solution. …”
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Some Properties of Motion Equations Describing the Nonlinear Dynamical Response of a Multibody System with Flexible Elements by Maria Luminiţa Scutaru, Sorin Vlase

“…Finally, second-order differential equations with variable coefficients are obtained; these equations are strong nonlinear ones due to the time-dependent values of angular speed and acceleration, and they can be linearized considering a very short period of time, in which the motion is considered to be “frozen.” …”
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Numerical Study on Resistance Change Characteristics of Phase Change Materials by Yifang Su, Yihang Zhang, Kaifeng Lin, Guanjun Zhao, Qinzheng Yu, Zuoqi Hu, Xiongfei Tao

“…To study the characteristics of the phase change materials, a numerical simulation model of the resistive change unit based on the finite element method and the classic nucleation/growth theory is established, while the partial differential equations of electricity and heat conduction and the discrete formula of the finite element are also derived. …”
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Role of stability analysis and waste discharge concentration of ternary hybrid nanofluid in a non-Newtonian model with slip boundary conditions by Nurhana Mohamad, Shuguang Li, Umair Khan, Anuar Ishak, Ali Elrashidi, Mohammed Zakarya

“…The suitable similarity transformations are utilized to transform the partial differential equations (PDEs) into ordinary differential equations (ODEs). …”
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Non Linear Thermal Radiation Analysis of Electromagnetic Chemically Reacting Ternary Nanofluid Flow over a Bilinear Stretching Surface by Shobha V, Hasan Mulki, Baskar P, S. Suresh Kumar Raju, Saleh Mahmoud, Mostafa Abdrabboh, S.V.K. Varma

“…Methodology: The governing nonlinear partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using similarity transformations. …”
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Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System by Alejandro Marquez, Jairo José Espinosa Oviedo, Darci Odloak

“…Around these optimal profiles, the nonlinear partial differential equations (PDEs), that model the reactor are linearized, and afterwards the linear PDEs are discretized in space giving as a result a high-order linear model. …”
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A simple model of carcinogenic mutations with time delay and diffusion by Monika Joanna Piotrowska, Urszula Foryś, Marek Bodnar, Jan Poleszczuk

“…In the paper we consider a system of delay differential equations (DDEs) of Lotka-Volterra type with diffusion reflecting mutations from normal to malignant cells. …”
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Mathematical modelling and dynamic optimization of phase-locked loop systems using hybrid PSO-gradient descent approach by Mrinal Kanti Rajak, Rajen Pudur

“…A comprehensive mathematical model is developed, incorporating the nonlinear dynamics of the PLL system through differential equations and transfer functions. The hybrid optimization framework is formulated as a constrained optimization problem, where PSO provides global search capabilities while GD ensures local convergence. …”
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Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators by Dongyuan Liu, Zigen Ouyang, Huilan Wang

“…Using Banach contraction mapping principle and Leray-Schauder continuation principle, we obtain some sufficient conditions for the existence and uniqueness of the positive solutions for the above fractional order differential equations, which extend some references.…”
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An efficient technique to study of time fractional Whitham–Broer–Kaup equations by Nishant Bhatnagar, Kanak Modi, Lokesh Kumar Yadav, Ravi Shanker Dubey

“…The method’s novelty and straightforward implementation establish it as a reliable and efficient analytical technique for solving both linear and nonlinear fractional partial differential equations.…”
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Dynamic Characteristics of a Cylindrical Roller Bearing with Cage Cracks by Yang Yang, Xiaoye Qi, Yongjie Wang, Meiling Wang, Baogang Wen, Jingyu Zhai

“…The derived dynamic differential equations of cylindrical roller bearings were solved by means of the modified Newton–Raphson iterative algorithm and the BDF predictive correction algorithm with automatic variable order and step length. …”
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MHD Heat and Mass Transfer of Chemical Reaction Fluid Flow over a Moving Vertical Plate in Presence of Heat Source with Convective Surface Boundary Condition by B. R. Rout, S. K. Parida, S. Panda

“…The basic equations governing the flow, heat transfer, and concentration are reduced to a set of ordinary differential equations by using appropriate transformation for variables and solved numerically by Runge-Kutta fourth-order integration scheme in association with shooting method. …”
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STABILITY RESEARCH OF FLOW-INDUCED VIBRATION OF HYBRID RIGID-FLEXIBLE PIPE CONVEYING FLUID (MT) by LIU MingJun, ZHANG ZhenJiu, YANG XianQing, Lü JianXing, LI YueAn

“…Based on Hamilton′s principle, the governing equations of motion of the hybrid rigid-flexible pipe system were established. The partial differential equations of motion were discretized via Galerkin′s approach using the modal functions of a cantilevered beam. …”
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Novel analytical superposed nonlinear wave structures for the eighth-order (3+1)-dimensional Kac-Wakimoto equation using improved modified extended tanh function method by Wafaa B. Rabie, Hamdy M. Ahmed, Taher A. Nofal, E. M. Mohamed

“…Higher-order nonlinear partial differential equations, such as the eighth-order Kac-Wakimoto model, are useful for studying wave turbulence in fluids, where energy transfers across a range of wave numbers. …”
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Modeling and analysis of the San Francisco City Clinic Cohort (SFCCC) HIV-epidemic including treatment by Brandy Rapatski, Juan Tolosa

“…We investigate two HIV/AIDS epidemic models.The first model represents the early San Franciscomen having sex with men (MSM) epidemic.We use data from the San Francisco City Clinic Cohort Study (SFCCC), documentingthe onset of HIV in San Francisco (1978-1984).The second model is a ``what-if'' scenario model includingtesting and treatment in the SFCCC epidemic.We use compartmental, population-level models,described by systems ofordinary differential equations.We find the basic reproductive number $R_0$ for each system,and we prove that if $R_0<1 the="" system="" has="" only="" the="" disease-free="" equilibrium="" dfe="" which="" is="" locally="" and="" globally="" stable="" whereas="" if="" r_0="">1$, the DFE is unstable.In addition, when $R_0>1$, both systems have a unique endemic equilibrium (EE).We show that treatment alone would not have stopped the San Francisco MSM epidemic,but would have significantly reduced its impact.…”
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Adaptive control of single-input single-output hybrid systems possessing interacting discrete- and continuous-time dynamics by M. de la Sen

“…As a result there are also mixed continuous-time and discrete signals present in the system associated either with the solutions of differential equations which depend at the same time on both discrete-time and continuous-time forcing terms and on generalized difference equations associated with discretized and digital signals. …”
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