A High Accuracy Spatial Reconstruction Method Based on Surface Theory for Regional Ionospheric TEC Prediction by Jian Wang, Yi‐ran Liu, Ya‐fei Shi

“…The core theory of this method is as follows: (a) Any surface can be uniquely determined by its first and second fundamental quantities; (b) By direct difference approximation, differential equations are transformed into algebraic equations to solve Gauss equations faster. …”
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Identification of a simplified mathematical model of an unmanned aerial vehicle by A. A. Lobaty, Y. F. Yatsyna, S. S. Prohorovith, Y. A. Hvitko

“…The analytical substantiation of the need to apply the methods of linearization of the mathematical model of UAV movement and the accepted assumptions for obtaining differential equations of UAV movement relative to the center of mass, allowing to synthesize the required transfer function of the corresponding element of the UAV control system. …”
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Advanced Method for Calculations of Core Burn-Up, Activation of Structural Materials, and Spallation Products Accumulation in Accelerator-Driven Systems by A. Stankovskiy, G. Van den Eynde

“…Secondly, it uses a state-of-the-art numerical solver for the first-order ordinary differential equations describing the isotope balances, namely, a Radau IIA implicit Runge-Kutta method. …”
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Nonlinear Hydroelastic Waves beneath a Floating Ice Sheet in a Fluid of Finite Depth by Ping Wang, Zunshui Cheng

“…The present formulas, different from the perturbation solutions, are highly accurate and uniformly valid without assuming that these nonlinear partial differential equations (PDEs) have small parameters necessarily. …”
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Hydrodynamic Boundary Layer Flow of Chemically Reactive Fluid over Exponentially Stretching Vertical Surface with Transverse Magnetic Field in Unsteady Porous Medium by M. Sulemana, I. Y. Seini, O. D. Makinde

“…The flow problem is modelled as time depended dimensional partial differential equations which are transformed to dimensionless equations and solved by means of approximate analytic method. …”
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New super and shock like solitary structures for KdV equation with higher-order nonlinearity by H.S. Alayachi, Abdulghani Alharbi, E.K. El-Shewy, Mahmoud A.E. Abdelrahman

“…The modified F-expansion approach is an effective, powerful and straightforward method for obtaining the solitary wave solutions to the nonlinear partial differential equations (NPDEs). The effect of model parameters on the nature, properties and structures of the model solutions have been examined. …”
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Bifurcation and controller design in a 3D delayed predator-prey model by Jinting Lin, Changjin Xu, Yiya Xu, Yingyan Zhao, Yicheng Pang, Zixin Liu, Jianwei Shen

“…This paper determines the parameter conditions for system stability and the occurrence of bifurcations by employing bifurcation theory and the stability theory of delayed differential equations. Using two control strategies, namely the mixed controller and the extended delay feedback controller, this paper effectively adjusts the stability domain of the delayed predator-prey systems and controls the time of bifurcation onset. …”
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Numerical Solutions of Certain New Models of the Time-Fractional Gray-Scott by Sami Aljhani, Mohd Salmi Md Noorani, Khaled M. Saad, A. K. Alomari

“…The fractional homotopy analysis transformation method algorithm can be easily applied for singular and nonsingular fractional derivative with partial differential equations, where a few terms of series solution are good enough to give an accurate solution.…”
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Super class of implicit extended backward differentiation formulae for the numerical integration of stiff initial value problems by Hamisu Musa, Buhari Alhassan

“…An implicit Superclass of non-block Extended Backward Differentiation Formulae (SEBDF) for the numerical integration of first-order stiff system of Ordinary Differential Equations (ODEs) in Initial Value Problems (IVPs) with optimal stability properties is presented. …”
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Applying Fourier Neural Operator to insect wingbeat sound classification: Introducing CF-ResNet-1D by Béla J. Szekeres, Máté Natabara Gyöngyössy, János Botzheim

“…Despite recent advancements in Deep Learning, Fourier Neural Operators (FNO), efficient for solving Partial Differential Equations due to their global spectral representations, have yet to be thoroughly explored for real-world time series classification or regression tasks. …”
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Jeffrey fluid flow past inclined stretchable sheet with magnetic dipole and suction/injection by Iyoko M.O., Olajuwon B.I., Fagbemiro O., Raji M.T.

“…The applicable equations were changed into nonlinear ordinary differential equations by similarity transformations. With the Chebyshev spectral collocation approach, solutions were obtained for fluid velocity and temperature. …”
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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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Optical soliton solutions of the M-fractional paraxial wave equation by Md. Habibul Bashar, Md. Abde Mannaf, M. M. Rahman, Mst. Tania Khatun

“…The strategy introduced is fundamental and robust as a smart soliton solution for nonlinear partial differential equations, and it may play a crucial role in nonlinear optics, fiber optics, and communication systems.…”
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Synchronous Stability of Four Homodromy Vibrators in a Vibrating System with Double Resonant Types by Xueliang Zhang, Chao Li, Zhihui Wang, Shiju Cui

“…This paper aims at studying the synchronous stability of four homodromy vibrators in subresonant and superresonant states. The motion differential equations are established firstly. The simplified form of analytical expressions is yielded, and the stability criterion of synchronous states satisfies Routh–Hurwitz criterion. …”
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A Novel Neural Network-Based Approach Comparable to High-Precision Finite Difference Methods by Fanghua Pei, Fujun Cao, Yongbin Ge

“…Deep learning methods using neural networks for solving partial differential equations (PDEs) have emerged as a new paradigm. …”
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A Qualitative Approach to Universal Numerical Integrators (UNIs) with Computational Application by Paulo M. Tasinaffo, Luiz A. V. Dias, Adilson M. da Cunha

“…The UNIs are used to model non-linear dynamic systems governed by Ordinary Differential Equations (ODEs). Among the main types of UNIs existing in the literature, we can mention (i) The Euler-Type Universal Numerical Integrator (E-TUNI), (ii) The Runge-Kutta Neural Network (RKNN), and (iii) The Non-linear Auto Regressive Moving Average with Exogenous input or NARMAX model. …”
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A Fuzzy Delay Approach for HIV Dynamics Using a Cellular Automaton by R. Motta Jafelice, C. A. F. Silva, L. C. Barros, R. C. Bassanezi

“…The objective of this research is to study the evolution of CD4+ T lymphocytes infected with HIV in HIV-seropositive individuals under antiretroviral treatment utilizing a mathematical model consisting of a system of delay-differential equations. The infection rate of CD4+ T lymphocytes is a time-dependent parameter with delay. …”
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Modeling and optimal regulation of erythropoiesis subject to benzene intoxication by H. T. Banks, Cammey E. Cole, Paul M. Schlosser, Hien T. Tran

“…An age-structured model was usedto examine the process of erythropoiesis, the development of red blood cells.This investigation proved the existence and uniqueness of the solution of thesystem of coupled partial and ordinary differential equations. In addition, weformulated an optimal control problem for the control of erythropoiesis andperformed numerical simulations to compare the performance of the optimalfeedback law and another feedback function based on the Hill function.…”
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Holographic reconstruction of black hole spacetime: machine learning and entanglement entropy by Byoungjoon Ahn, Hyun-Sik Jeong, Keun-Young Kim, Kwan Yun

“…Utilizing neural ordinary differential equations alongside Monte-Carlo integration, we develop a method tailored for continuous training functions to extract the general isotropic bulk metric from entanglement entropy data. …”
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Evolution-Operator-Based Single-Step Method for Image Processing by Yuhui Sun, Peiru Wu, G. W. Wei, Ge Wang

“…The key component of the proposed method is a local spectral evolution kernel (LSEK) that analytically integrates a class of evolution partial differential equations (PDEs). From the point of view PDEs, the LSEK provides the analytical solution in a single time step, and is of spectral accuracy, free of instability constraint. …”
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