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.…”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

Strength Analysis for Cage of Planetary Wheel Needle Roller Bearing by Yubo Wang, Haisheng Yang, Manjun Xu, Yongcun Cui, Sier Deng

“…Aiming to solving the problem of cage failure under revolution-rotation，based on the dynamics theory of rolling bearing，the dynamics differential equations of needle roller bearing coupled with revolution-rotation working condition are established，and GSTIFF variable step length integral algorithm is adopted to solve the bearing. …”
Get full text

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. …”
Get full text

Douglas' Factorization Theorem and Atomic System in Hilbert Pro-$C^{\ast}$-Modules by Mohamed Rossafi, Roumaissae Eljazzar, Ram Mohapatra

Get full text

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. …”
Get full text

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. …”
Get full text

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)”.…”
Get full text

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. …”
Get full text

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. …”
Get full text

ANALYSIS OF THE INTERNAL RESONANCE CHARACTERISTICS OF RECTANGULAR CURRENT-CONDUCTING THIN PLATE IN TRANSVERSE MAGNETIC FIELD by LI Jing, HU YuDa

“…According to a rectangular plate with one side fixed and three other sides simply supported,time variable and space variable are separated by the displacement modal expansion and the method of Galerkin,and the two-degree-of-freedom internal resonance nonlinear vibration differential equations are obtained. By the method of multiple scales,the coupled characteristic equations of the first two order vibration modes are obtained under the case of 1∶3 internal resonance. …”
Get full text

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. …”
Get full text

Representation of the solution of a nonlinear molecular beam epitaxy equation by Boubaker Smii

“…Stochastic partial differential equations (SPDEs) driven by Lévy noise are extensively employed across various domains such as physics, finance, and engineering to simulate systems experiencing random fluctuations. …”
Get full text

Threshold dynamics of stochastic SIRSW infectious disease model with multiparameter perturbation by Zhengwen Yin, Yuanshun Tan

“…In addition to establishing the existence and uniqueness of the global positive solution of the model, we derived the threshold conditions for the extinction and persistence of the disease using the comparison theorem and It$ \hat{o} $'s formula of stochastic differential equations. Subsequently, we obtained the asymptotic stability of both the disease-free equilibrium and the endemic equilibrium of the deterministic model corresponding to the stochastic model through stochastic stability theory. …”
Get full text