Duality Identities for Moduli Functions of Generalized Melvin Solutions Related to Classical Lie Algebras of Rank 4 by S. V. Bolokhov, V. D. Ivashchuk

“…The solution is governed by four moduli functions Hs(z) (s=1,…,4) of squared radial coordinate z=ρ2 obeying four differential equations of the Toda chain type. These functions turn out to be polynomials of powers (n1,n2,n3,n4)=(4,6,6,4),(8,14,18,10),(7,12,15,16),(6,10,6,6) for Lie algebras A4, B4, C4, and D4, respectively. …”
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Application of fluid dynamics in modeling the spatial spread of infectious diseases with low mortality rate: A study using MUSCL scheme by Nnaji Daniel Ugochukwu, Kiogora Phineas Roy, Onah Ifeanyi Sunday, Mung’atu Joseph, Aguegboh Nnaemeka Stanley

“…By treating susceptible, infected, and treated population densities as fluids governed by a system of partial differential equations, the study simulates the epidemic’s spatial dynamics. …”
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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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Preliminary Hybrid Modeling of the Panama Canal: Operations and Salinity Diffusion by Luis Rabelo, Mario Marin, Petros Xanthopoulos, Carlos Arellano Lennox, Pedro Coiduras, Bernardo Campos, Luz Andrade, Ricardo Collins, Erwin Atencio, Daryelis Pitty

“…This was accomplished by generating an operational discrete-event simulation model and a continuous simulation model based on differential equations, which modeled the salinity diffusion in the lakes. …”
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Forecasting Crude Oil Consumption in China Using a Grey Prediction Model with an Optimal Fractional-Order Accumulating Operator by Huiming Duan, Guang Rong Lei, Kailiang Shao

“…In this paper, we study the grey-extended SIGM model, which is directly estimated with differential equations. This model has high simulation and prediction accuracies and is one of the important models in grey theory. …”
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Theoretical Analysis and Experimental Validation on Galloping of Iced Transmission Lines in a Moderating Airflow by Bing Huo, Xuliang Li, Fujiang Cui, Shuo Yang

“…Galloping of an iced transmission line subjected to a moderating airflow has been analysed in this study, and a new form of galloping is discovered both theoretically and experimentally. The partial differential equations of the iced transmission line are established based on the Hamilton theory. …”
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Reconstruction of self-oscillating systems with delay time modulation by Ponomarenko, Vladimir Ivanovich, Prokhorov, Mihail Dmitrievich

“…The object of study is self-oscillating systems described by delay-differential equations, in which the delay time is modulated by an external periodic signal. …”
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Computational Role of Autocatalytic Chemical Reaction in the Dynamics of a Ternary Hybrid Nanofluid Past a Rotating Stretching Surface by Shreedevi Madiwal, N. B. Naduvinamani, J. K. Madhukesh, Umair Khan, Anuar Ishak, Raman Kumar, Md Irfanul Haque Siddiqui

“…The governing equations are transformed into the system of ordinary differential equations (ODEs) and numerically tackled with the help of the Runge–Kutta–Fehlberg 4th 5th (RKF45) order scheme. …”
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On optimization of substrate removal in a bioreactor with wall attached and suspended bacteria by Alma Mašić, Hermann J. Eberl

“…In the two-objective optimal control problem, the flow rate between the vessels is selected as the control variable.The treatment reactor is modelled by a system of three ordinary differential equations in which a two-point boundary value problem is embedded. …”
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Second-Order Systems of ODEs Admitting Three-Dimensional Lie Algebras and Integrability by Muhammad Ayub, Masood Khan, F. M. Mahomed

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A frictional contact problem with normal damped response conditions and thermal effects for a thermo-electro-viscoelastic material by Abdelmoumene Djabi

“…The author establishes the existence of a unique weak solution to the problem by utilizing classical results for evolutionary quasivariational elliptic inequalities, parabolic differential equations and fixed point arguments. Design/methodology/approach – The author establishes a variational formulation for the model and proves the existence of a unique weak solution to the problem using classical results for evolutionary quasivariational elliptic inequalities, parabolic difierential equations and fixed point arguments. …”
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A novel Bessel–Newton algorithm for the simulation of 2D laminar flow between two moving porous walls problem by Atallah El-shenawy, Mohamed El-Gamel, Muhammad E. Anany

“…The difficulty resides in precisely and effectively solving the governing nonlinear differential equations that characterize such flows. We propose a unique Bessel–Newton algorithm that utilizes the Bessel operational matrices collocation method for discretizing the equations and employs a Newton iterative strategy to resolve the resulting nonlinear system. …”
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On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China by Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger

“…In 1986, a mathematical model based on ordinary differential equations was introduced to take into account the distribution of sexual activity. …”
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Predictive Model for Deformation of Adjacent Pipelines Caused by Tunnel Boring in Twin-Lane Tunnels in Soft Ground Layers by Kezhong Wang, Qianjiang Zheng, Maowen Hang

“…To create a discretized prediction model for the deformation of an adjacent pipeline, the pipeline structure is discretized, the differential equations governing the longitudinal deformation of the pipeline are inferred, and the displacement expressions and the solution methods of the virtual nodes of each unit are provided after discretization. …”
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Development of an information measuring and control system for a quadrocopter by V. V. Sleptsov, V. L. Afonin, A. E. Ablaeva, Ba Phuong Dinh

“…The coordinate systems (fixed and mobile) and the kinematic scheme are given, according to which a system of differential equations is presented. The system describes the dynamics of the quadrocopter movement and takes into account the expected smooth movement of the quadrocopter with small roll and pitch angles. …”
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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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Entropy framework of the bioconvective Williamson nanofluid flow over a Riga plate with radiation, triple stratification and swimming microorganisms by K. Loganathan, N. Thamaraikannan, S. Eswaramoorthi, Reema Jain

“…Utilizing a suitable conversion approach, translate the partial differential equation (PDEs) system into ordinary differential equations (ODEs). …”
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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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Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filtering by Gerasimos G. Rigatos, Efthymia G. Rigatou, Jean Daniel Djida

“…The intracellular protein synthesis dynamic model is described by a set of coupled nonlinear differential equations. It is shown that such a dynamical system satisfies differential flatness properties and this allows to transform it, through a change of variables (diffeomorphism), to the so-called linear canonical form. …”
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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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