Positive Position Feedback Control for High-Amplitude Vibration of a Flexible Beam to a Principal Resonance Excitation by Li Jun

“…The perturbation method of multiple scales is employed to find the general nonlinear response of the system and four first-order differential equations governing the amplitudes and phases of the responses are derived. …”
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Binary mixture convection in a horizontal channel under the Soret effect action by Stepanova Irina

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Nonlinear iterative approximation of steady incompressible chemically reacting flows by Gazca-Orozco, Pablo Alexei, Heid, Pascal, Süli, Endre

“…We consider a system of nonlinear partial differential equations modelling steady flow of an incompressible chemically reacting non-Newtonian fluid, whose viscosity depends on both the shear-rate and the concentration; in particular, the viscosity is of power-law type, with a power-law index that depends on the concentration. …”
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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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Simulating Smoke Filling in Big Halls by Computational Fluid Dynamics by W. K. Chow, C. L. Chow, S. S. Li

“…Mathematical aspects concerning of discretization of partial differential equations and algorithms for solving the velocity-pressure linked equations are briefly outlined. …”
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An extension of Gompertzian growth dynamics: Weibull and Fréchet models by J. Leonel Rocha, Sandra M. Aleixo

“…These models, described by differential equations, are proportional to the hyper-Gompertz growth model. …”
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A toxin-mediated size-structured population model: Finite difference approximation and well-posedness by Qihua Huang, Hao Wang

“…Motivated by the fact that individuals with different sizes may have different sensitivities to toxins, we develop a toxin-mediated size-structured model which is given by a system of first order fully nonlinear partial differential equations (PDEs). It is very possible that this work represents the first derivation of a PDE model in the area of ecotoxicology. …”
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Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems by D. Baleanu, A. H. Bhrawy, T. M. Taha

“…We present a direct solution technique for approximating linear multiterm fractional differential equations (FDEs) on semi-infinite interval, using generalized Laguerre polynomials. …”
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An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs by Eman S. Alaidarous, Malik Zaka Ullah, Fayyaz Ahmad, A.S. Al-Fhaid

“…The reported method is very general and can be extended to desired order of convergence for highly nonlinear differential equations and also computationally superior to proposed iterative method based on Adomain decomposition because our proposed iterative scheme avoids the calculations of Adomain polynomials and achieves the same computational order of convergence as authors have claimed in Motsa and Sibanda, 2013. …”
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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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Simple Ion Transfer at Liquid|Liquid Interfaces by L. J. Sanchez Vallejo, J. M. Ovejero, R. A. Fernández, S. A. Dassie

“…We describe numerical simulations implementing different approaches for solving the differential equations associated with the mass transport and charge transfer. …”
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PDE Modeling of a Microfluidic Thermal Process for Genetic Analysis Application by Reza Banaei Khosroushahi, Horacio J. Marquez, Jose Martinez-Quijada, Christopher J. Backhouse

“…The general partial differential equations describing the dynamics of the system are separated into steady-state and transient parts which are derived for a carefully chosen three-dimensional axisymmetric model. …”
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The Inverse Problem of Identification of Hydrogen Permeability Model by Yury V. Zaika, Natalia I. Rodchenkova, Ekaterina K. Kostikova

“…A numerical method is developed for TDS spectrum simulation, where only integration of a nonlinear system of low order ordinary differential equations is required. The main final output of the article is a noise-resistant algorithm for solving the inverse problem of parametric identification for the aggregated experiment where desorption and diffusion are dynamically interrelated (without the artificial division of studies into the diffusion limited regime (DLR) and the surface limited regime (SLR)).…”
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On the Fractional View Analysis of Keller–Segel Equations with Sensitivity Functions by Haobin Liu, Hassan Khan, Rasool Shah, A. A. Alderremy, Shaban Aly, Dumitru Baleanu

“…The suggested procedure is very attractive and straight forward and therefore can be modified to solve high nonlinear fractional partial differential equations and their systems.…”
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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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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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Dynamic Model of a Rotating Flexible Arm-Flexible Root Mechanism Driven by a Shaft Flexible in Torsion by S.Z. Ismail, A.A. Al-Qaisia, B.O. Al-Bedoor

“…The obtained model is a nonlinear-coupled system of differential equations. The model is simulated for different combinations of shaft and root flexibilities and arm properties. …”
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Starlikeness associated with certain strongly functions by Afis Saliu, Kanwal Jabeen, Jianhua Gong, Sarfraz Nawaz Malik, Hala Alaqad

“…It also finds the solutions to first-order differential equations and utilizes these results together with the differential subordination developed by Miller and Mocanu to obtain the conditions so that some first-order differential relations associated with ϕλ are subordinate to certain Ma and Minda functions. …”
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Analyzing Axial Stress and Deformation of Tubular for Steam Injection Process in Deviated Wells Based on the Varied (T,P) Fields by Yunqiang Liu, Jiuping Xu, Shize Wang, Bin Qi

“…The varied temperature and pressure fields were researched by the coupled differential equations concerning mass, momentum, and energy equations instead of traditional methods. …”
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Adaptive Synchronization for Two Different Stochastic Chaotic Systems with Unknown Parameters via a Sliding Mode Controller by Zengyun Wang, Lihong Huang, Xuxin Yang, Dingyang Lu

“…Firstly, based on the Lyapunov theory in stochastic differential equations and the theory of sliding mode control, we propose a simple sliding surface and discuss the occurrence of the sliding motion. …”
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