A Direct Eulerian GRP Scheme for the Prediction of Gas-Liquid Two-Phase Flow in HTHP Transient Wells by Jiuping Xu, Min Luo, Jiancheng Hu, Shize Wang, Bin Qi, Zhiguo Qiao

“…A coupled system model of partial differential equations is presented in this paper, which concerns the variation of the pressure and temperature, velocity, and density at different times and depths in high temperature-high pressure (HTHP) gas-liquid two-phase flow wells. …”
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A Vieta–Lucas collocation and non-standard finite difference technique for solving space-time fractional-order Fisher equation by Mohd Kashif

“…By using the properties of Vieta–Lucas polynomials, this technique reduces the nonlinear equations into a system of ordinary differential equations (ODEs). The non-standard finite difference (NSFD) method converts this system of ODEs into algebraic equations which have been solved numerically. …”
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Novel Numerical Scheme for Singularly Perturbed Time Delay Convection-Diffusion Equation by Mesfin Mekuria Woldaregay, Worku Tilahun Aniley, Gemechis File Duressa

“…This paper deals with numerical treatment of singularly perturbed parabolic differential equations having large time delay. The highest order derivative term in the equation is multiplied by a perturbation parameter ε, taking arbitrary value in the interval 0,1. …”
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Dynamic Response of Parallel Hoisting System under Drive Deviation between Ropes with Time-Varying Length by Guohua Cao, Xiang Cai, Naige Wang, Weihong Peng, Jishun Li

“…The slack situation of the rope is considered, and the dynamic equations which are systems of DAEs are transformed to ordinary differential equations (ODEs). The dynamic responses of tension, torsion, and acceleration are analyzed considering radius’ error of the drums, which indicates that the drive deviation between ropes can cause large influence on the tension difference and even cause one of the ropes to slack. …”
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Numerical Simulations of the Square Lid Driven Cavity Flow of Bingham Fluids Using Nonconforming Finite Elements Coupled with a Direct Solver by R. Mahmood, N. Kousar, M. Yaqub, K. Jabeen

“…All these implementations are done in the open source software package FEATFLOW which is a general purpose finite element based solver package for solving partial differential equations.…”
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Differential Quadrature Analysis of Free Vibration of Symmetric Cross-Ply Laminates with Shear Deformation and Rotatory Inertia by Moinuddin Malik, Charles W. Bert

“…By using the trigonometric functions describing the mode shapes between the simply supported edges, the governing plate equations are reduced to ordinary differential equations. The solution of the reduced equations is then sought by the differential quadrature method. …”
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Opposition to Synchronization of Bistable State in Motif Configuration of Rössler Chaotic Oscillator Systems by Dıdıer Lopez Mancılla, Guillermo Huerta-cuellar, Juan Hugo García López, Rider Jaimes-reategui

“…The study was conducted using the differential equations representing the piecewise linear Rössler-like electronic circuits; the initial conditions were changed to achieve a bistable characteristic Homoclinic H-type or Rössler R-type attractor. …”
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Effective Method for Analysis of Electrothermally Coupled Fields by Jacek Korytkowski, Stanisław Wincenciak

“…An effective method is presented for solving a nonlinear system of partial differential equations that describe the time-dependent electrothermally coupled fields for passage of constant electric current in a three-dimensional conductive medium. …”
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A multi-layer neural network-based evaluation of MHD radiative heat transfer in Eyring–Powell fluid model by Muflih Alhazmi, Zahoor Shah, Muhammad Asif Zahoor Raja, Nafisa A. Albasheir, Maryam Jawaid

“…To facilitate analysis, governing partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) only with the aid of similarity transformations. …”
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ANN-based two hidden layers computational procedure for analysis of heat transport dynamics in polymer-based trihybrid Carreau nanofluid flow over needle geometry by Adil Darvesh, Fethi Mohamed Maiz, Basma Souayeh, Luis Jaime Collantes Santisteban, Hakim AL. Garalleh, Afnan Al Agha, Lucerito Katherine Ortiz García, Nicole Anarella Sánchez-Miranda

“…These governing system is transformed into ordinary differential equations (ODEs) via appropriate similarity transformations. …”
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A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems by S. S. Motsa

“…The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. …”
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A One-Point Third-Derivative Hybrid Multistep Technique for Solving Second-Order Oscillatory and Periodic Problems by Mufutau Ajani Rufai, Ali Shokri, Ezekiel Olaoluwa Omole

“…This paper describes a third-derivative hybrid multistep technique (TDHMT) for solving second-order initial-value problems (IVPs) with oscillatory and periodic problems in ordinary differential equations (ODEs), the coefficients of which are independent of the frequency omega and step size h. …”
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Modeling colony collapse disorder in honeybees as a contagion by Christopher M. Kribs-Zaleta, Christopher Mitchell

“…The system of three ordinary differential equations accounts for multiple hive population behaviors including Allee effects and colony collapse. …”
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Douglas' Factorization Theorem and Atomic System in Hilbert Pro-$C^{\ast}$-Modules by Mohamed Rossafi, Roumaissae Eljazzar, Ram Mohapatra

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DYNAMIC MODEL OF THE BUDGET OF AN EDUCATIONAL INSTITUTION by Antonina V. Ganicheva, Aleksey V. Ganichev

“…Methodology: modeling, theory of solving differential equations. Results: a modified Keynes model has been developed, allowing for the calculation and optimization of the budget of educational organizations. …”
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Analysis and Enhancements of a Prolific Macroscopic Model of Epilepsy by Christopher Fietkiewicz, Kenneth A. Loparo

“…Specifically, we analyze three aspects of the models: (1) Using dynamical systems analysis, we demonstrate and explain the presence of direct current potentials in the simulated EEG that were previously undocumented. (2) We explain how the system was not ideally formulated for numerical integration of stochastic differential equations. A reformulated system is developed to support proper methodology. (3) We explain an unreported contradiction in the published model specification regarding the use of a mathematical reduction method. …”
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Improvement of Image Compression by Changing the Mathematical Equation Style in Communication Systems by Riyadh M. Al-Saleem, Yasameen A. Ghani, Shihab A. Shawkat

“…The test images for these patterns showed a discrepancy in the image resolution when the compression coefficient was increased, as the results using three types of image compression methods proved a clear superiority when using “partial differential equations (PDE)”.…”
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Evolution-Operator-Based Single-Step Method for Image Processing

“…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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A Mathematical Model for DNA Damage and Repair by Philip S. Crooke, Fritz F. Parl

“…The model encompasses a set of differential equations representing the sequence of enzymatic reactions in both damage and repair pathways. …”
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A High Order Theory for Linear Thermoelastic Shells: Comparison with Classical Theories by V. V. Zozulya

“…Then in the same way as in the 3D theories system of differential equations in terms of displacements and boundary conditions for Fourier coefficients has been obtained. …”
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