Improving diversification by a hybrid bat-Nelder-Mead algorithm and DDE for rapid convergence to solve global optimization by Enas Suhail, Mahmoud El-Alem, Omar Bazighifan, Ahmed Zekri

“…Delay differential equations and algorithms hold a crucial position in the exploration of some biological systems and several models in real-world applications. …”
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Insight on the complete process of photoacoustic generation and propagation of cerebrovascular in brain via multi-physics coupling method by Shangkun Hou, Anzhi Lv, Jiabin Lin, Bokang You, Shuaixin Huang, Xianlin Song

“…The diffusion equation is approximated by the partial differential equations in the form of coefficients in the mathematical module of COMSOL to describe laser propagation in brain tissue. …”
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Time-periodic dynamics in COVID-19 transmission considering the impact of population disbelief and fear by Mahmoud A. Ibrahim, Attila Dénes

“…Our model utilizes a system of differential equations that incorporates the impact of both contagious fear and contagious disbelief surrounding the disease on its transmission dynamics. …”
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A Novel Highly Nonlinear Quadratic System: Impulsive Stabilization, Complexity Analysis, and Circuit Designing by Arthanari Ramesh, Alireza Bahramian, Hayder Natiq, Karthikeyan Rajagopal, Sajad Jafari, Iqtadar Hussain

“…Most of the quadratic ordinary differential equations (ODEs) such as Chen, Rossler, and Lorenz have at least one linear term in their equations. …”
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Modeling and simulation for toxicity assessment by Cristina Anton, Jian Deng, Yau Shu Wong, Yile Zhang, Weiping Zhang, Stephan Gabos, Dorothy Yu Huang, Can Jin

“…We consider a three dimensional system of differential equations with variables corresponding to the cell index, the intracellular concentration of toxicant, and the extracellular concentration of toxicant. …”
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Dubovsky’s Class of Mathematical Models for Describing Economic Cycles with Heredity Effects by Danil Makarov, Roman Parovik, Zafar Rakhmonov

“…Dubovsky, consisting of two nonlinear differential equations of fractional order and describing the dynamics of the efficiency of new technologies and the efficiency of capital productivity, taking into account constant and variable heredity. …”
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Compartmental Models Driven by Renewal Processes: Survival Analysis and Applications to SVIS Epidemic Models by Divine Wanduku, Md Mahmud Hasan

“…The novel SVIS model is formulated as a non-autonomous nonlinear system (NANLS) of ordinary differential equations (ODEs), with coefficients defined by HRFs. …”
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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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An Accurate Measurement Method for Tension Force of Short Cable by Additional Mass Block by Shuichang Li, Longlin Wang, Hua Wang, Peihua Shi, Riyan Lan, Changxia Wu, Xirui Wang

“…By attaching an additional mass block to the cable, new parameters are introduced to identify the tension force. Vibration differential equations are established for cable with and without addition mass block, taking new parameters into account, such as equivalent effective length and added mass. …”
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Resolvent Positive Operators and Positive Fractional Resolvent Families by Nan-Ding Li, Ru Liu, Miao Li

“…Some examples of positive solutions to fractional differential equations are presented to illustrate our results.…”
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Cubic-quartic optical solitons with polarization-mode dispersion by the improved adomian decomposition scheme by Afrah M. Almalki, A.A. AlQarni, H.O. Bakodah, A.A. Alshaery, Ahmed H. Arnous, Anjan Biswas

“…This method decomposes both linear and nonlinear differential equations into simpler sub-problems, enabling the extraction of approximate analytical solutions without the need for linearization or perturbation techniques. …”
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Models for the spread and persistence of hantavirus infection in rodents with direct and indirect transmission by Curtis L. Wesley, Linda J. S. Allen, Michel Langlais

“…Two models are analyzed, a nonautonomous system of differential equations with time-periodic coefficients and an autonomous system, where the coefficients are taken to be the time-average. …”
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Parallel Simulation of HGMS of Weakly Magnetic Nanoparticles in Irrotational Flow of Inviscid Fluid by Kanok Hournkumnuard, Banpot Dolwithayakul, Chantana Chantrapornchai

“…The two-dimensional problem of particle transport under the influences of magnetic force and fluid flow is considered in an annular domain surrounding the wire with inner radius equal to that of the wire and outer radius equal to various multiples of wire radius. The differential equations governing particle transport are solved numerically as an initial and boundary values problem by using the finite-difference method. …”
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Unstructured Grids and the Multigroup Neutron Diffusion Equation by German Theler

“…It consists of a set of second-order partial differential equations over the spatial coordinates that are, both in the academia and in the industry, usually solved by discretizing the neutron leakage term using a structured grid. …”
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Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional Subdiffusion/Superdiffusion Equations by Meilan Qiu, Liquan Mei, Dewang Li

“…The numerical experiment results show that the fully discrete local discontinuous Galerkin (LDG) methods are efficient and powerful for solving fractional partial differential equations.…”
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Couple Stress Sodium Alginate-Based Casson Nanofluid Analysis through Fick’s and Fourier’s Laws with Inclined Microchannel by Dolat Khan, Musawa Yahya Almusawa, Waleed Hamali, M. Ali Akbar

“…Physically existent things utilize partial differential equations as a method of derivation. By using dimensionless variables, the underlying PDEs are dimensionless. …”
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MAC Layer Energy Consumption and Routing Protocol Optimization Algorithm for Mobile Ad Hoc Networks by Yaohua Chen, Waixi Liu

“…In order to solve the problem that the analytic solution of differential equations cannot be obtained in the model, a numerical solution of the optimization algorithm is proposed based on the implicit Runge–Kutta method. …”
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Implementing the Galerkin Method Associated with the Shifted Vieta-Lucas Polynomials for Studying Numerically the Bionanofluid Flow Which Is Saturated by Gyrotactic Microorganisms... by M. M. Khader, M. M. Babatin, Ahmed M. Megahed, A. Eid

“…The shifted Vieta-Lucas polynomials are then used as basis functions on the provided domain to solve the nonlinear system of ordinary differential equations that has been constructed (ODEs). The results are presented in the form of graphs and tables to assess the impact of the problem’s governing parameters. …”
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A Theoretical Model of Listeriosis Driven by Cross Contamination of Ready-to-Eat Food Products by C. W. Chukwu, F. Nyabadza

“…In this paper, a mathematical model that takes into consideration cross contamination of Listeria monocytogenes from a food processing plant environment is formulated using a system of ordinary differential equations. The model has three equilibria: the disease-free equilibrium, Listeria-free equilibrium, and endemic equilibrium points. …”
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Mixed Convection in a Double Lid-Driven Wavy Shaped Cavity Filled with Nanofluid Subject to Magnetic Field and Internal Heat Source by Kakali Chowdhury, Md. Abdul Alim

“…The physical problems are characterized by 2D governing partial differential equations accompanying proper boundary conditions and are discretized using Galerkin’s finite element formulation. …”
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