Mixed Convective-Radiative Dissipative Magnetized Micropolar Nanofluid Flow over a Stretching Surface in Porous Media with Double Stratification and Chemical Reaction Effects: ADM-... by P. K. Pattnaik, M. M. Bhatti, S. R. Mishra, Munawwar Ali Abbas, O. Anwar Bég

“…The nonlinear governing partial differential conservation equations are rendered into nonlinear ordinary differential equations via relevant transformations. An innovative semi-numerical methodology combining the Adomian decomposition method (ADM) with Padé approximants and known as ADM-Padé is deployed to solve the emerging nonlinear ordinary differential boundary value problem with appropriate wall and free stream conditions in MATLAB software. …”
Get full text

On the transitory performance of mixed convective heat and mass transfer around spherical region in the presence of fluctuating streams by Hossam A. Nabwey, Sahar Anwar, Muhammad Ashraf, A.M. Rashad

“…For this purpose, the coupled partial differential equations are first non-dimensionalized and their steady and oscillatory components are separated. …”
Get full text

Accelerated pseudo-transient method for elastic, viscoelastic, and coupled hydromechanical problems with applications by Y. Alkhimenkov, Y. Y. Podladchikov

“…<p>The accelerated pseudo-transient (APT) method is a matrix-free approach used to solve partial differential equations (PDEs), characterized by its reliance on local operations, which makes it highly suitable for parallelization. …”
Get full text

Formation of unmanned aircraft trajectory when flying around prohibited areas by A. A. Lobaty, A. Y. Bumai, A. M. Avsievich

“…A mathematical model of UAV motion in the horizontal plane is proposed, in the form of a system of ordinary differential equations in the Cauchy form. A law for measuring the control acceleration of the UAV’s center of mass is obtained on the basis of specifying the minimized quality functional and the corresponding constraints, which is a feature of the considered method of solving the problem. …”
Get full text

Investigating nonlinear dynamic properties of an inertial sensor with rotational velocity-dependent rigidity by Mina Ghanbari, Mohammad Fathalilou, Hamed Haddad Khodaparast, Ghader Rezazadeh

“…The numerical Galerkin approach is employed for discretization of the coupled differential equations in spatial coordinates. To obtain the sensor response as a function of frequency, a continuation arc-length method based on weak formulation energy balance method is used. …”
Get full text

Nonlinear Dynamic Response Analysis of Cable–Buoy Structure Under Marine Environment by Qiufu Xie, Binghan Liu, Junxian Zhang, Yaobing Zhao

“…To address these challenges, this study derives coupled differential equations for the cable–buoy structure based on the two drag force models. …”
Get full text

A Fluid Model for Mobile Data Offloading Based on Device-to-Device Communications with Time Constraints by Antonio Pinizzotto, Raffaele Bruno

“…To address this issue, we propose a novel fluid model based on ordinary differential equations (ODEs) for the performance analysis of a general D2D-based mobile data offloading scheme, called OORS, which considers both content delivery guarantees and time limitations for storing content copies in local device caches, making it more practical for real-world applications. …”
Get full text

How Do Diabetes Models Measure Up? A Review of Diabetes Economic Models and ADA Guidelines by Lindsay Govan, Olivia Wu, Robert Lindsay, Andrew Briggs

“…There are four main types of models: Markov-based cohort, Markov-based microsimulations, discrete-time microsimulations, and continuous time differential equations. All models were long-term diabetes models incorporating a wide range of compilations from various organ systems. …”
Get full text

Dynamic analysis and comparison of the performance of linear and nonlinear controllers applied to a nonlinear non-interactive and interactive process by José M. Campos-Salazar, Pablo Lecaros, Rodrigo Sandoval-García

“…The process dynamics were initially modeled using nonlinear differential equations, which were subsequently linearized to facilitate the design of the PI and LQR controllers. …”
Get full text

Estimated effect of rotational components of seismic impact on the strength-strain state of simple systems by O. V. Mkrtychev, A. A. Reshetov, E. M. Lokhova

“…In the scope of this study, the rotational components of accelerograms are obtained from both the action of only one translational component and from the action of two translational components of seismic action for an integral seismic motion model; and the equation of motion has been derived considering them.Materials and methods. The differential equations of motion for the investigated systems were solved in both planar and spatial settings. …”
Get full text

A ternary hybrid model for analysis of enhanced heat transport in non-Newtonian nanofluid over cylindrical geometry with effect of infinite shear rate viscosity by Hakim AL Garalleh

“…Based on assumptions of current study, the governing partial differential equations (PDEs) are formed and then transformed into ODEs for numerical solution. …”
Get full text

Investigation of Heat and Mass Transfer in the Process of Fuel Preparation from Biomass Particles with High Moisture by A. V. Mitrofanov, O. B. Kolibaba, R. N. Gabitov, D. A. Dolinin, S. V. Vasilevich

“…In the course of the study, the following tasks were solved: a numerical method was developed for describing the processes of internal and external heat and mass transfer problems using an explicit difference approximation of differential equations of heat and mass transfer; parametric identification of the proposed one-dimensional mathematical model was performed using empirical dependencies known from literature sources; empirical verification of the proposed mathematical model was carried out by comparing the calculated forecasts obtained with the results of their own field experiments. …”
Get full text

A Novel Numerical Treatment to One Dimensional Heat and Wave Equations with Second Order Accuracy by Muhammad Abid, Muhammad Shahid

“…Numerical solutions to partial differential equations (PDEs) play a vital role in modeling complex physical phenomena across scientific computing and engineering disciplines. …”
Get full text

Qualitative financial modelling in fractal dimensions by Rami Ahmad El-Nabulsi, Waranont Anukool

“…Abstract The Black–Scholes equation is one of the most important partial differential equations governing the value of financial derivatives in financial markets. …”
Get full text

A Mathematical Model for the Growth Dynamics of Demand in the Fashion Industry within the Era of the COVID-19 Pandemic by John Awuah Addor, Anthony Joe Turkson, Douglas Yenwon Kparib

“…A five-compartment susceptible-infection-recovery-susceptible-based model was formulated in an integrated environment with application of fashion-based personal protective equipment (FPPEs) and government policy regulation, using ordinary differential equations. Solution techniques included a mix of qualitative analysis and simulations with data from various publications on COVID-19. …”
Get full text

Magnetohydrodynamic Peristaltic Propulsion of Casson Nanofluids With Slip Effects Over Heterogeneous Rough Channel by Hanumesh Vaidya, Fateh Mebarek‐Oudina, Rakesh Kumar, C. Rajashekhar, Kerehalli Vinayaka Prasad, Sangeeta Kalal, Kottakkaran Sooppy Nisar

“…A novel rough non‐uniform model is effectively governed by a set of nonlinear coupled governing partial differential equations, which are simplified under long wavelength and creeping flow approximations. …”
Get full text

Extrapolation of cavitation and hydrodynamic pressure in lubricated contacts: a physics-informed neural network approach by Faras Brumand-Poor, Freddy Kokou Azanledji, Nils Plückhahn, Florian Barlog, Lukas Boden, Katharina Schmitz

“…In particular, physics-informed neural networks (PINNs) are as effective hybrid solvers that combine data-driven and physics-based methods to solve the partial differential equations that drive EHL simulations. By integrating physical laws into the parameter optimization of the neural network (NN), PINNs provide accurate and fast solutions. …”
Get full text

Models for an arenavirus infection in a rodent population: consequences of horizontal, vertical and sexual transmission by Chandrani Banerjee, Linda J. S. Allen, Jorge Salazar-Bravo

“…We formulate a general deterministic model for male and female rodents consisting of eight differential equations, four for females and four for males. …”
Get full text

Ion homeostasis in the regulation of intracellular pH and volume of human erythrocytes by О. І. Доценко, Г. В. Тарадіна

“…Material and Methods: The mathematical model was developed using general approaches to modeling cellular metabolism, which are based on systems of ordinary differential equations describing metabolic reactions, passive and active ion fluxes. …”
Get full text

Displacement of hydrocarbon liquids by water using the models of zonally heterogeneous deformable formations by Marat Ya. Khabibullin, Rustem I. Suleymanov, Razifa R. Stepanova, Alina Az. Gizzatullina, Arsen M. Khabibullin

“…It is known that the motion of two-phase hydrocarbon systems in deformable reservoirs is represented by complex nonlinear partial differential equations. An analytical solution of such equations is possible only with the use of special approaches. …”
Get full text