341 Results Found

This article considers heat transfer in a solid body with temperature-dependent thermal conductivity that is in contact with a tank filled with liquid. The liquid in the tank is heated by hot liquid entering the tank through a pipe. Liquid at a lower...

In this paper we study an ODE model for the interaction between nature and society where the system dynamics is driven largely by the social wealth. The relevant variables are renewable resources, non-renewable ones, and wealth, while population depe...

We discuss different approaches for the analytical description of a mechanical system used in control theory, aiming at the analytical modelling of experimental artefacts observed in the implementation of ideal searched trajectories. Starting from an...

The velocity of air that crosses the canopy of tree crops when using orchard sprayers is a variable that affects pesticide dispersion in the environment. Therefore, having an equation to describe air velocity decay through the canopy is of interest....

Optical solitons have emerged as a highly active research domain in nonlinear fiber optics, driving significant advancements and enabling a wide range of practical applications. This study investigates the dynamics of dark solitons in systems governe...

This article explains how discrete symmetry groups can be directly applied to obtain the particular solutions of nonlinear ordinary differential equations (ODEs). The particular solutions of some nonlinear ordinary differential equations have been ge...

This paper deals with several nonlinear partial differential equations (PDEs) of mathematical physics such as the concatenation model (perturbed concatenation model) from nonlinear fiber optics, the plane hydrodynamic jet theory, the Kadomtsev–...

Origin–destination (OD) passenger flow is a critical variable for metro system planning and operation. While numerous studies have investigated the influence of the built environment on passenger flow, most have focused on ingress or egress flo...

In this paper, we introduce an ODE system to model the interaction between natural resources and human exploitation in a rich consumeristic society. In this model, the rate of change in population depends on wealth per capita, and the rate of consump...

This paper deals with the stabilization of a class of uncertain nonlinear ordinary differential equations (ODEs) with a dynamic controller governed by a linear $1-d$ heat partial differential equation (PDE). The control operates at one boundary o...

The development of simple and yet accurate formulations of frequency–amplitude relationships for non-conservative nonlinear oscillators is an important issue. The present paper is concerned with integral-type frequency–amplitude formulas...

This paper is concerned with solving the problem of identifying the control vector problem for a fractional multi-order system of nonlinear ordinary differential equations (ODEs). We describe a quasilinearization approach, based on minimization of a...

In this article, we take into account the $(2+1)$-dimensional stochastic Chiral nonlinear Schrödinger equation (2D-SCNLSE) in the Itô sense by multiplicative noise. We acquired trigonometric, rational and hyperbolic stochastic exact solution...

This paper provides several illustrations of the numerous remarkable properties of the lambda extensions of the two-point correlation functions of the Ising model, shedding some light on the non-linear ODEs of the Painlevé type they satisfy. W...

Study of swinging clapper bells involves aspects encompassing sound and acoustic engineering, mechanical engineering, and structural engineering. From the musical point of view, clapper bells are directly played idiophone instruments, where the playi...

To address physical problems that require solving differential equations, both linear and nonlinear analytical methods are preferred when possible, but numerical methods are utilized when necessary. In this study, the normalization technique is estab...

The present manuscript proposes a computational approach to efficiently tackle a class of two-point boundary value problems that features third-order nonlinear ordinary differential equations. Specifically, this approach is based upon a combination o...

In engineering, physics, and other fields, implicit ordinary differential equations are essential to simulate complex systems. However, because of their intrinsic nonlinearity and difficulty separating higher-order derivatives, implicit ordinary diff...

Recently, direct methods that involve higher derivatives to numerically approximate higher order initial value problems (IVPs) have been explored, which aim to construct numerical methods with higher order and very high precision of the solutions. Th...

The current study aims to utilize the homotopy perturbation method (HPM) to solve nonlinear dynamical models, with a particular focus on models related to predicting and controlling pandemics, such as the SIR model. Specifically, we apply this method...

Tuberculosis (TB) has a long history as a serious disease induced by its causative agent Mycobacterium tuberculosis. This pathogen manipulates the host’s immune response, thereby stimulating inflammatory processes, which leads to an even greate...

In this paper, we consider nonlinear integration techniques, based on direct Padé approximation of the differential equation solution, and their application to conservative chaotic initial value problems. The properties of discrete maps obtain...

In this manuscript, we find the numerical solutions of a class of fractional-order differential equations with singularity and strong nonlinearity pertaining to electrohydrodynamic flow in a circular cylindrical conduit. The nonlinearity of the under...

To cut a clod of soil containing the roots of trees in nurseries, a semi-circular vibrating blade digging machine with diameters up to 1.2 m is increasingly used. The heart of the machine is the mechanical oscillator that produces an excitation torqu...

A novel time-dependent deterministic SEIRS model, extended with vaccination, hospitalization, and vital dynamics, is introduced. Time-varying basic and effective reproduction numbers associated with this model are defined, which are crucial metrics i...

Background: This work presents a mechanistic nonlinear model, formulated as a system of first-order Ordinary Differential Equations, to investigate the dynamics of Chronic Lymphocytic Leukemia (CLL) under combined chemoimmunotherapy using CAR-T cells...

The estimation of the network traffic state, its likely short-term evolution, the prediction of the expected travel times in a network, and the role that mobility patterns play in transport modeling is usually based on dynamic traffic models, whose m...

In this paper, some geometric properties of the plane interception curve defined by a nonlinear ordinary differential equation are discussed. Its parametric representation is used to find the limits of some triangle elements associated with the curve...

The properties of the entropy production in convecting–radiating fins were analyzed. By taking advantage of the explicit expression for the distribution of heat along the fin, we investigated the possibility of assessing the efficiency of these...

The purpose of this paper is to investigate a system of differential equations related to the viscous flow over a stretching sheet. It is assumed that the intended environment for the flow includes a chemical reaction and a magnetic field. The govern...

We present a novel indicator for the effectiveness of longitudinal, convecting-radiating fins to dissipate heat. Starting from an analysis of the properties of the entropy rate of the steady state, we show how it is possible to assess the efficiency...

In this paper, we introduce a new three-step Newton method for solving a system of nonlinear equations. This new method based on Gauss quadrature rule has sixth order of convergence (with $n=3$). The proposed method solves nonlinear boundary-value prob...

In this paper, we introduce two new methods to solve systems of ordinary differential equations. The first method is constituted of the generalized Bernstein functions, which are obtained by Bernstein polynomials, and operational matrix of differenti...

This paper summarizes a mathematical model for the industrial heating and cooling processes of a steel workpiece corresponding to the steering rack of an automobile. The general purpose of the heat treatment process is to create the necessary hardnes...

The paper presents an analytical solution for the centric viscoelastic impact of two smooth balls. The contact period has two phases, compression and restitution, delimited by the moment corresponding to maximum deformation. The motion of the system...

Data from the World Health Organization indicate that Bulgaria has the second-highest COVID-19 mortality rate in the world and the lowest vaccination rate in the European Union. In this context, to find the crucial epidemiological parameters that cha...

This paper introduces a novel SEIRS-type differential model that incorporates significant real-world factors such as vaccination, hospitalization, and vital dynamics. The model is described by a system of nonlinear ordinary differential equations wit...

The study considers a nonlinear multi-parameter reaction–diffusion system of two Lotka–Volterra-type equations with several delays. It treats both cases of different diffusion coefficients and identical diffusion coefficients. The study d...

This article presents a new prediction model, the ordinary differential equations–memory kernel function (ODE–MKF), constructed from multiple backtracking initial values (MBIV). The model is similar to a simplified numerical model after s...

In this paper, we analytically study the two-dimensional unsteady irrotational flow of an ideal incompressible fluid in a half-plane whose boundary is assumed to be a linear sink. It is shown that the nonlinear evolution of perturbations of the initi...

In this manuscript, by using undetermined parameter method, an efficient iterative method with eighth-order is designed to solve nonlinear systems. The new method requires one matrix inversion per iteration, which means that computational cost of our...

A novel nonlinear dynamic modeling approach is proposed for the T-shaped beam structures widely used in the field of aerospace. All of the geometrical nonlinearities including the terms in the deformation of the beams, the terms at the connections, a...

A dynamic model of an L-shaped multi-beam joint structure is presented to investigate the nonlinear dynamic behavior of the system. Firstly, the nonlinear partial differential equations (PDEs) of motion for the beams, the governing equations of the t...

This study addresses heat and mass transfer of electrical magnetohydrodynamics (MHD) Williamson fluid flow over the moving sheet. The mathematical model for the considered flow phenomenon is expressed in a set of partial differential equations. Later...

In this work, we investigate invariance analysis, conservation laws, and exact power series solutions of time fractional generalized Drinfeld–Sokolov systems (GDSS) using Lie group analysis. Using Lie point symmetries and the Erdelyi–Kober (EK) fract...

This paper addresses a numerical approach for computing the solitary wave solutions of the generalized Rosenau–Kawahara–RLW model established by coupling the generalized Rosenau–Kawahara and Rosenau–RLW equations. The solution of this model is accomp...

A family of third-order partial differential equations (PDEs) is analyzed. This family broadens out well-known PDEs such as the Korteweg-de Vries equation, the Gardner equation, and the Burgers equation, which model many real-world phenomena. Further...

Continuous Time Echo State Networks (CTESNs) are a promising yet under-explored surrogate modeling technique for dynamical systems, particularly those governed by stiff Ordinary Differential Equations (ODEs). A key determinant of the generalization a...

In this paper Pade Embedded Differential Transformation is proposed for the solution of higher order nonlinear or linear Ordinary Differential Equations (ODE’s). The proposed approach provides a better iterative procedure to find the spectrum of the...

This entry examines Lorenz’s error growth models with quadratic and cubic hypotheses, highlighting their mathematical connections to the non-dissipative Lorenz 1963 model. The quadratic error growth model is the logistic ordinary differential e...