Comparative Studies of Nonlinear Models and Their Applications to Magmatic Evolution and Crustal Growth of the Huai’an Terrane in the North China Craton by Qiuming Cheng, Min Gao

“…This paper introduces these nonlinear functions derived from a unified differential equation, with parameters that reflect their relative nonlinearities and singularities, enabling their comparative application. …”
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Research on Constriction Resistance of Drum Gear Coupling of High Speed EMU by Chunjun Chen, Xiang Zheng, Lu Yang, Linchun Zhou

“…Make use of the load distribution method to calculate the relationship between the load of each tooth and the total load of the coupling according to the flexural approximate differential equation of single tooth，according to the Hertz contact theory and the rough surface contact theory，the actual contact area and constriction resistance are calculated. …”
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Analysis of Bianchi Type V Holographic Dark Energy Models in General Relativity and Lyra’s Geometry by Daba Meshesha Gusu, M. Vijaya Santhi

“…The solutions of differential equation fields have been obtained by considering two specific cases, namely, the expansion scalar θ in the model is proportional to the shear scalar σ and the average scale factor taken as hybrid expansion form. …”
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Numerical Solutions of Duffing Van der Pol Equations on the Basis of Hybrid Functions by M. Mohammadi, A. R. Vahidi, T. Damercheli, S. Khezerloo

“…The next technique is to convert this equation into a system of ordinary differential equation of the first order (SODE) and solve it according to the proposed approximate method. …”
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Trivariate Stochastic Weather Model for Predicting Maize Yield by Patrick Chidzalo, Phillip O. Ngare, Joseph K. Mung’atu

“…Stochastic analyses are applied on the pdf and process to account for nonlinearity and nonstationarity, and also establish a corresponding stochastic differential equation (SDE) for maize yield. The trivariate stochastic process predicts maize yield with R2=0.8389 and MAPE=4.31% under a deep learning framework. …”
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Financial development, research in finance, and economic growth by Chadi Azmeh, Marwan Al-Raeei

“…Utilizing the two-step system GMS method and the Runge-Kutta framework, the research defines and addresses a differential equation, achieving remarkable precision in economic modeling by fine-tuning step sizes and adapting the algorithm to the specific economic context. …”
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Numerical Simulation of Dynamic Response of Submerged Floating Tunnel under Regular Wave Conditions by Wenlong Luo, Bo Huang, Yao Tang, Hao Ding, Ke Li, Liang Cheng, Qingyang Ren

“…In this model, wave-induced hydrodynamic loads are estimated by the Morison equation for a moving object, and the simplified governing differential equation of the tunnel with mooring cables is solved using the fourth-order Runge–Kutta and Adams numerical method. …”
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Nonlinear compressive reduced basis approximation for PDE’s by Cohen, Albert, Farhat, Charbel, Maday, Yvon, Somacal, Agustin

“…Linear model reduction techniques design offline low-dimensional subspaces that are tailored to the approximation of solutions to a parameterized partial differential equation, for the purpose of fast online numerical simulations. …”
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Heat and mass transfer performance of power-law nanofluid flow with thermal radiation and joule heating aspects: Surface heat flux analysis by Mhamed Benaissa, Zia Ullah, A. Dahshan, Md Mahbub Alam, Khadijah M. Abualnaja, Hanaa Abu-Zinadah, Abdullah A. Faqihi, Nidhal Ben Khedher

“…The physical problems are converted into a nonlinear ordinary differential equation under the implementation of similarity transformations, stream functions and Keller box method. …”
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Measurement of Coordinated and Coupled Development and Evaluation of Sustainable Development for Marine Economic-Ecological Complex System by Mingming Wen, Chang Liu, K. A. Mamonov, Jun Du

“…Specifically, an ecology-dominated coordinated development model was proposed for the complex system, and a differential equation model was established to describe the dynamic coordinated development of the complex system. …”
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Probing the diversity of kink solitons in nonlinear generalised Zakharov-Kuznetsov-Benjamin-Bona-Mahony dynamical model by Naher Mohammed A. Alsafri, Hamad Zogan

“…Using a wave transformation, the employed transformative technique first converts GZK-BBME to a nonlinear ordinary differential equation (NODE). With the incorporation of the Riccati equation, a close-form solution is then assumed for the resultant NODE by RMESEM, which converts the NODE into a set of algebraic equations. …”
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Modeling and Dynamic Performance Analysis of Hydraulic Top Drive Main Transmission System with Long Hydraulic Pipelines by Yuanling Shi, Pingsong Zhang

“…A mathematical model of hydraulic top drive main transmission with differential equation of hydraulic units and state space equation of hydraulic long pipelines was deduced in this research. …”
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Large-Eddy Simulation of the Flow Past a Circular Cylinder at Re = 130,000: Effects of Numerical Platforms and Single- and Double-Precision Arithmetic by Dmitry A. Lysenko

“…Numerical simulations of sub-critical flow past a circular cylinder at Reynolds number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mi mathvariant="normal">R</mi><mi mathvariant="normal">e</mi></mrow></mrow></semantics></math></inline-formula> = 130,000 are performed using two numerical platforms: the commercial, Ansys Fluent, and the open-source, OpenFOAM (finite volume method and large-eddy simulation based on a differential equation for the sub-grid kinetic energy). An overview of the available experimental data and similar large-eddy simulation studies is presented. …”
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Mathematical Analysis of Malaria Epidemic: Asymptotic Stability With Cost-Effectiveness Study by Sacrifice Nana-Kyere, Baba Seidu, Kwara Nantomah

“…With the ongoing vaccination programs for vector-borne diseases, the research proposes a nonlinear differential equation model for the malaria disease that provides public health with a shift from the classical understanding of nonpharmaceutical preventive malaria control to pharmaceutical measures of vaccines. …”
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Multiple Positive Solutions of Singular Nonlinear Sturm-Liouville Problems with Carathéodory Perturbed Term by Yuefeng Han, Xinguang Zhang, Lishan Liu, Yonghong Wu

“…By employing a well-known fixed point theorem, we establish the existence of multiple positive solutions for the following fourth-order singular differential equation Lu=p(t)f(t,u(t),u′′(t))-g(t,u(t),u′′(t)),0<t<1,α1u(0)-β1u'(0)=0,γ1u(1)+δ1u'(1)=0,α2u′′(0)-β2u′′′(0)=0,γ2u′′(1)+δ2u′′′(1)=0, with αi,βi,γi,δi≥0 and βiγi+αiγi+αiδi>0,    i=1,2, where L denotes the linear operator Lu:=(ru′′′)'-qu′′,r∈C1([0,1],(0,+∞)), and q∈C([0,1],[0,+∞)). …”
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Study on Quality Decisions in Supply Chain considering the Lagged Time and Retailers Competition by Yuan Peng, Liang Ning

“…This paper probes into the lagged time of quality on goodwill under the competitive environment of retailers and constructs a lagged differential equation of quality on goodwill based on the Nerlove–Arrow model. …”
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On the Optimal Control of HIV-TB Co-Infection and Improvement of Workplace Productivity by Baba Seidu, Oluwole Daniel Makinde, Ibrahim Yakubu Seini

“…In this paper, we present a nonlinear ordinary differential equation model to study the dynamics of HIV-TB co-infection and its effect on workforce productivity. …”
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Neural ODEs for holographic transport models without translation symmetry by Zhuo-Fan Gu, Yu-Kun Yan, Shao-Feng Wu

“…We convert the flow equation to a Neural Ordinary Differential Equation (Neural ODE), which is a neural network with continuous depth and produces output through a black-box ODE solver. …”
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Application of Adaptive Image Restoration Algorithm Based on Sparsity of Block Structure in Environmental Art Design by Bo Liang, Xin-xin Jia, Yuan Lu

“…This paper proposes a color image restoration method that adaptively determines the size of dictionary atoms and discusses a model based on the partial differential equation restoration method. Through simulation experiments combined with subjective and objective standards, the repair results are evaluated and analyzed. …”
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μ Robust Stable Extrapolation of a Stationary Random Process with Interval Limited Variance by Igor G. Sidorov

“…This approach, unlike others (for example, probabilistic), always ensures the existence of a stable result and solution of a single optimum in the problem of interval minimax extrapolation due to regularization by a small parameter with a derivative of the eigenfunction of a singularly perturbed integro-differential equation of the first order with an integral operator of the Voltaire type of the second kind, defined by a symmetric, closed real the core. …”
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