Anani Kwassi | Searcharxiv

arXiv2026

Group reduction, formulas solutions and asymptotic behavior of a class of fourth order difference equations

The symmetry method is a powerful and systematic approach for solving difference equations. It leverages the concept of transformations that leave a difference equation invariant, simplifying its structure and often reducing the equation to a solvable form. In this paper, the symmetry method is employed to study some class of difference equations. Using analytical techniques and computational tools, we derive explicit solutions for these equations and establish conditions for the existence of periodic solutions. Stability analysis is performed to identify non-hyperbolic points. Furthermore, some asymptotic properties of the difference equations are explored, with results and graphs illustrating how initial conditions and parameter values influence the behavior of the solutions.

math.DS↗

arXiv2023

Analytical approximations in short times of exact operational solutions to reaction diffusion problems on bounded intervals

This paper aims at obtaining, by means of integral transforms, analytical approximations in short times of solutions to boundary value problems for the one-dimensional reaction-diffusion equation with constant coefficients. The general form of the equation is considered on a bounded generic interval and the three classical types of boundary conditions, i.e., Dirichlet as well as Neumann and mixed boundary conditions are considered in a unified way. The Fourier and Laplace integral transforms are successively applied and an exact solution is obtained in the Laplace domain. This operational solution is proven to be the accurate Laplace transform of the infinite series obtained by the Fourier decomposition method and presented in the literature as solutions to this type of problem. On the basis of this unified operational solution, four cases are distinguished where innovative formulas expressing consistent analytical approximations in short time limits are derived with respect to the behavior of the solution at the boundaries. Compared to the infinite series solutions, the analytical approximations may open new perspectives and applications, among which can be noted the improvement of numerical efficiency in simulations of one-dimensional moving boundary problems, such as in Stefan models.

math.AP↗