A New Approach to Black Hole Quasinormal Modes: A Review of the Asymptotic Iteration Method by H. T. Cho, A. S. Cornell, Jason Doukas, T.-R. Huang, Wade Naylor

“…We discuss how to obtain black hole quasinormal modes (QNMs) using the asymptotic iteration method (AIM), initially developed to solve second-order ordinary differential equations. We introduce the standard version of this method and present an improvement more suitable for numerical implementation. …”
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Theoretical investigation on models of circadian rhythms based on dimerization and proteolysis of PER and TIM by Jifa Jiang, Qiang Liu, Lei Niu

“…By imposing assumptions that the dimerization reactions were fast and dimeric proteins were in rapid equilibrium, they reduced the model to a pair of nonlinear ordinary differential equations of mRNA and total protein concentrations. …”
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Elasticity Solutions for Sandwich Arches considering Permeation Effect of Adhesive by Ruili Huo, Yichen Liu, Peng Wu, Hai Fang, Weiqing Liu, Ding Zhou

“…The governing equations of the arch are solved by the layer-wise method, which turns the differential equations with variable coefficients into constant coefficients. …”
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Nonlinear Dynamics Analysis of the Wind Turbine Gear Transmission System Considering Friction Effect by Xu Fan, Liu Wenbin, Zhang Haibo, Zhang Qiang, Wu Shijing, Wang Xiaosun, Duan Jiujun

“…After nondimensionalization, the dynamics differential equations are obtained. Runge-Kutta methods are adopted to solve equations and the nonlinear dynamic response of the wind turbine gear transmission system is acquired. …”
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A Mathematical and Numerically Integrable Modeling of 3D Object Grasping under Rolling Contacts between Smooth Surfaces by Suguru Arimoto, Morio Yoshida

“…A set of 1st-order differential equations governing rotational motions of each fingertip and the object and updating arc-length parameters should be accompanied with the Euler-Lagrange equations. …”
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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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Mathematical Modeling of Coccidiosis Dynamics in Chickens with Some Control Strategies by Yustina A. Liana, Mary C. Swai

“…Using the theory of differential equations, the invariant set of the model was derived, and the model’s solution was found to be mathematically and biologically significant. …”
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A Reduced Order Model Based on ANN-POD Algorithm for Steady-State Neutronics and Thermal-Hydraulics Coupling Problem by Hanxing Liu, Han Zhang

“…Due to the high-dimensional partial differential equations (PDEs) derived from the N/TH system, it is usually time consuming to solve such a large-scale nonlinear equation by the traditional numerical solution method of PDEs. …”
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Artificial neural networks for stability analysis and simulation of delayed rabies spread models by Ramsha Shafqat, Ateq Alsaadi

“…This study addressed the complexity of rabies spread by integrating two critical delay effects—vaccination efficacy and incubation duration—into a delay differential equations model, capturing more realistic infection patterns between dogs and humans. …”
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Effects of Thermodiffusion and Chemical Reaction on Magnetohydrodynamic-Radiated Unsteady Flow Past an Exponentially Accelerated Inclined Permeable Plate Embedded in a Porous Mediu... by B. Prabhakar Reddy, M. H. Simba, Alfred Hugo

“…The governing nondimensional set of coupled nonlinear partial differential equations with related initial and boundary conditions are solved numerically by using the accurate and efficient DuFort–Frankel’s explicit finite difference method. …”
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Analysis of Fractional-Order Regularized Long-Wave Models via a Novel Transform by Nehad Ali Shah, Essam R. El-Zahar, Ali Akgül, Adnan Khan, Jeevan Kafle

“…In fact, when compared to other analytical techniques for solving nonlinear fractional partial differential equations, the present method might be considered one of the finest.…”
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The Feyn-structure of Yangian symmetry by Florian Loebbert, Harshad Mathur

“…Previous applications of the Yangian suggest to employ the resulting differential equations for bootstrapping multi-loop integrals beyond the dual conformal case. …”
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On Regularization of an Optimal Control Problem for Ill-Posed Nonlinear Elliptic Equations by Peter I. Kogut, Olha P. Kupenko, Rosanna Manzo

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Characterization of the dynamic behavior of nonlinear biosystems in the presence of model uncertainty using singular invariance PDEs: Application to immobilized enzyme and... by Nikolaos Kazantzis, Vasiliki Kazantzi

“…The problem of interest is addressed within the context of singular partial differential equations (PDE) theory, and in particular, through a system of singular quasi-linear invariance PDEs for which a general set of conditions for solvability is provided. …”
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Conciliating accuracy and efficiency to empower engineering based on performance: a short journey by Chinesta, Francisco, Cueto, Elias

“…The art of modeling for describing the behavior of complex systems from the solution of partial differential equations that are expected to govern their responses. …”
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Qualitative Properties of the Solution of a Conjugate Problem of Thermal Convection by A. A. Azanov, E. N. Lemeshkova

“…Thus, the problem was reduced to a system of 10 nonlinear integro-differential equations. Its conjugate and inverse nature is determined by the four functions of time. …”
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Hopf Bifurcation, Cascade of Period-Doubling, Chaos, and the Possibility of Cure in a 3D Cancer Model by Marluci Cristina Galindo, Cristiane Nespoli, Marcelo Messias

“…We study a cancer model given by a three-dimensional system of ordinary differential equations, depending on eight parameters, which describe the interaction among healthy cells, tumour cells, and effector cells of immune system. …”
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Numerical Study on Resistance Change Characteristics of Phase Change Materials by Yifang Su, Yihang Zhang, Kaifeng Lin, Guanjun Zhao, Qinzheng Yu, Zuoqi Hu, Xiongfei Tao

“…To study the characteristics of the phase change materials, a numerical simulation model of the resistive change unit based on the finite element method and the classic nucleation/growth theory is established, while the partial differential equations of electricity and heat conduction and the discrete formula of the finite element are also derived. …”
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Development of a Family of Chaotic Systems with Infinite Equilibria and Its Application for Image Encryption by Xiaofeng Li, Yulong Bai, Weishuan Pan, Di Wang, Yong-Jie Ma

“…Fourth-order autonomous nonlinear differential equations can exhibit chaotic properties. In this study, we propose a family of fourth-order chaotic systems with infinite equilibrium points whose equilibria form closed curves of different shapes. …”
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Raves, clubs and ecstasy: the impact of peer pressure by Baojun Song, Melissa Castillo-Garsow, Karen R. Ríos-Soto, Marcin Mejran, Leilani Henso, Carlos Castillo-Chavez

“…In this study, a system of differential equations is used to model the peer-driven dynamics of ecstasy use. …”
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