in this paper, we study the boundedness and persistence of the solutions, the global stability of the unique positive equilibrium point and the rate of convergence of a solution that converges to the equilibrium $e=(bar{x}, bar{y})$ of the system of two difference equations of exponential form: begin{equation*} x_{n+1}=dfrac{a+e^{-(bx_n+cy_n)}}{d+bx_n+cy_n}, y_{n+1}=dfrac{a+e^{-(by_n+cx_n)}}{d+...

In this paper, the exponential B-spline functions are used for the numerical solution of the advection-diffusion equation. Two numerical examples related to pure advection in a finitely long channel and the distribution of an initial Gaussian pulse are employed to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies.

We study the behavior of exponential random graphs in both the sparse and the dense regime. We show that exponential random graphs are approximate mixtures of graphs with independent edges whose probability matrices are critical points of an associated functional, resulting in a matrix equation. In the dense regime, every solution to this equation is close to a block matrix, concluding that the...

In this paper, we mainly introduced a definition of moment exponential stability for multifactor uncertain differential equation. For illustrating of stability concept, several examples and counterexamples are given. Furthermore, a necessary and sufficient condition of stability in pth moment exponential of linear multifactor uncertain differential equation is obtained. Also, the necessary and ...

Exponential solutions of the Yang-Baxter equation give rise to generalized Schubert polynomials and corresponding symmetric functions. We provide several descriptions of the local stationary algebra defined by this equation. This allows to construct various exponential solutions of the YBE. The Bn and G2 cases are also treated.

‎We study the existence of soliton solutions for a class of‎ ‎quasilinear elliptic equation in $mathbb{textbf{R}}^2$ with critical exponential growth‎. ‎This model has been proposed in the self-channeling of a‎ ‎high-power ultra short laser in matter‎.

SEIR epidemiological models with the inclusion of quarantine and isolation are used to study the control and intervention of infectious diseases. A simple ordinary differential equation (ODE) model that assumes exponential distribution for the latent and infectious stages is shown to be inadequate for assessing disease control strategies. By assuming arbitrarily distributed disease stages, a ge...

In this paper, I explore the exponential Rosenbrock-type method of order two. It is an explicit method that solves stiff ODEs. The method linearizes the equation with each step, then uses a matrix exponential to solve the linearized equation exactly. Previous research has identified stability bounds and convergence results. In this paper, I explore the stiffness capabilities of this second orde...