Solutions of Cauchy Problems for the Caudrey–Dodd–Gibbon–Kotera–Sawada Equation in Three Spatial and Two Temporal Dimensions by Yufeng Zhang, Linlin Gui

“…Fokas has obtained integrable nonlinear partial differential equations (PDEs) in 4 + 2 dimensions by complexifying the independent variables. …”
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Explicit scheme based on integral transforms for estimation of source terms in diffusion problems in heterogeneous media by André José Pereira de Oliveira, Luiz Alberto da Silva Abreu, Diego Campos Knupp

“… The estimation of source terms present in differential equations has various applications, ranging from structural assessment, industrial process monitoring, equipment failure detection, environmental pollution source detection to identification applications in medicine. …”
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Influence of different delays on mixed types of oscillations under limited excitation by A. A. Alifov

“…With the account of the interaction with the energy source, the known calculation scheme (or model) of a mechanical frictional self-oscillating system serves as a unified basis for considering all types of MOs. Nonlinear differential equations of motion valid for all types of MOs with their respective solutions were presented, from which the relations for any certain type of MO are derived as special cases. …”
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Evaluation of the increased load bearing capacity of steel beams strengthened with pre-stressed FRP laminates by S. Bennati, D. Colonna, P.S. Valvo

“…The model is described by a set of differential equations with suitable boundary conditions. …”
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Nonlinear Dynamics of the High-Speed Rotating Plate by Minghui Yao, Li Ma, Wei Zhang

“…Galerkin approach is applied to discretize the partial differential governing equations of motion to ordinary differential equations. Asymptotic perturbation method is exploited to derive four-degree-of-freedom averaged equation for the case of 1 : 3 internal resonance-1/2 sub-harmonic resonance. …”
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An individual-level probabilistic model and solution for control of infectious diseases by Ye Xia

“…The model is related to the work of Fraser et al. on the same topic [1], which provides a population-level model using a combination of differential equations and probabilistic arguments. We show that our individual-level model has certain advantages. …”
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INFLUENCE OF THE TIME OF DISINHIBITION TO TRANSIENTS AND WEAR OF THE FRICTION LININGS IN AN ASYNCHRONOUS MOTOR by V. V. Solencov, V. V. Brel

“…Calculation of the system of differential equations was fulfilled by the Runge – Kutta method. …”
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In Silico Evolution of Gene Cooption in Pattern-Forming Gene Networks by Alexander V. Spirov, Marat A. Sabirov, David M. Holloway

“…Finally, we comment on how a differential equations (in contrast to Boolean) approach is necessary for addressing realistic continuous variation in biochemical parameters.…”
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Stability, Bifurcation, and a Pair of Conserved Quantities in a Simple Epidemic System with Reinfection for the Spread of Diseases Caused by Coronaviruses by Jorge Fernando Camacho, Cruz Vargas-De-León

“…In this paper, we study a modified SIRI model without vital dynamics, based on a system of nonlinear ordinary differential equations, for epidemics that exhibit partial immunity after infection, reinfection, and disease-induced death. …”
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An in-depth examination of the fuzzy fractional cancer tumor model and its numerical solution by implicit finite difference method. by Hamzeh Zureigat, Saleh Alshammari, Mohammad Alshammari, Mohammed Al-Smadi, M Mossa Al-Sawallah

“…Researchers have employed fractional differential equations to describe these models. In the context of time fractional cancer tumor models, there's a need to introduce fuzzy quantities instead of crisp quantities to accommodate the inherent uncertainty and imprecision in this model, giving rise to a formulation known as fuzzy time fractional cancer tumor models. …”
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Numerical and analytical investigation of Jeffrey nanofluid convective flow in magnetic field by FEM and AGM by Mohammad ِDehghan Afifi, Ali Jahangiri, Mohammad Ameri

“…Solving and developing non-linear differential equations is done using finite element method (FEM) and Akbari-Ganji method (AGM). …”
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NONLINEAR CHARACTERISTICS OF HERRINGBONE GEAR FOUR-BRANCHING TRANSMISSION CONSIDERING GEAR BACKLASH EFFECT by DONG Hao, FANG ZongDe, FANG Zhou, ZHAO XiaoLong

“…With herringbone gear loaded tooth contact method of simulation technology,put forward a method for accurate calculation of herringbone gear meshing stiffness excitation; By using the theory of the concentrated parameter,three-dimensional dynamic model of bending torsion coupling of the system is established;Based on the dynamic differential equations are solved with variable step four order Runge-Kutta method,obtained under the influence of backlash in the system without impact,dynamic load coefficient and amplitude of unilateral and bilateral shock state.The results show that Power four branch transmission system has a complex nonlinear characteristic,which is sensitive to the change of the tooth side gap,the influence of the backlash on the nonlinear characteristics is greater,and the system load changes from the side impact to the side impact of the system when the backlash is changed from 0 μm 150 μm; When the tooth gap is greater than a certain critical value,the dynamic characteristics of the system will not change with the increase of the gap of the tooth. …”
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Mathematical insights on psoriasis regulation: Role of Th1 and Th2 cells by Amit Kumar Roy, Priti Kumar Roy, Ellina Grigorieva

“…In this article, we have constructed a set of nonlinear differential equations involving the above cell population for better understanding the impact of cytokines on Psoriasis. …”
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Nonlinear Autoregressive Neural Network for Antimicrobial Waste Water Treatment by Anwer Mustafa Hilal, Mashael M. Asiri, Shaha Al-Otaibi, Faisal Mohammed Nafie, Amal Al-Rasheed, Mohammed Rizwanullah, Ishfaq Yaseen, Abdelwahed Motwakel

“…Dirichlet design parameters and a combined combination of Neumann and Dirichlet boundary situation are applied to the system of differential equations. In addition, the proposed method use the learning under supervision technique of a nonlinear autoregressive for estimating the CO2 concentration and flows in units of rate of a reaction characteristics, an exogenous (NARX) neural network model with two activation functions was used (Log-sigmoid and hyperbolic tangent) and for both the findings of a TC and SMX absorption simulations showed the random forest performed support vector tree and nonlinear autoregressive exogenous neural networks and machine learning methods. …”
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Differential game theory application in models of trade relations of Great Britain with Portugal and Russia with Belarus by I. V. Korolyov

“…The author composes and analyzes a system of four nonlinear ordinary differential equations with parameters, and their (dynamic) variation leads to the improvement of successive approximations of the exact solution, the finding of which is very problematic. …”
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Asymptotical Behavior of the Solution of a SDOF Linear Fractionally Damped Vibration System by Z.H. Wang, M. L. Du

“…The solutions of the initial value problems of linear fractional differential equations are usually expressed in terms of Mittag-Leffler functions or some other kind of power series. …”
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A Methodology for Practical Design and Optimization of Class-E DC-DC Resonant Converters by Andrea Celentano, Fabio Pareschi, Victor R. Gozalez-Diaz, Riccardo Rovatti, Gianluca Setti

“…Its peculiarity is to be dimensionless and based on the exact solution of the system of differential equations regulating the behavior of the circuit, ensuring very high precision and reliability with respect to all methodologies previously proposed by the state-of-the-art and based on the so-called sinusoidal approximation. …”
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What can mathematical models tell us about the relationship between circular migrations and HIV transmission dynamics? by Aditya S. Khanna, Dobromir T. Dimitrov, Steven M. Goodreau

“…We construct models from each class, usingordinary differential equations and exponential random graph models,respectively. …”
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Radionuclide Transport in Fractured Rock: Numerical Assessment for High Level Waste Repository by Claudia Siqueira da Silveira, Antonio Carlos Marques Alvim, Jose de Jesus Rivero Oliva

“…Transport in the fracture is assumed to obey an advection-diffusion equation, while molecular diffusion is considered the dominant mechanism of transport in porous matrix. The partial differential equations describing the movement of radionuclides were discretized by finite difference methods, namely, fully explicit, fully implicit, and Crank-Nicolson schemes. …”
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Modeling and 1 : 1 Internal Resonance Analysis of Cable-Stayed Shallow Arches by Jiangen Lv, Zhicheng Yang, Xuebin Chen, Quanke Wu, Xiaoxia Zeng

“…Firstly, the Galerkin method is used to discretize the governing nonlinear integral-partial-differential equations. Secondly, the multiple scales method (MSM) is used to derive the modulation equations of the system under external excitation of the shallow arch. …”
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