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Mensah Folly-Gbetoula

Publications and source records attributed to Mensah Folly-Gbetoula.

10 recordsLinked to original sources
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↗
arXiv2026

Exact solution to a class of problems for the Burgers' equation on bounded intervals

Burgers' equation with fixed Dirichlet boundary conditions is considered on generic bounded intervals. By using the Hopf-Cole transformation and the exact operational solution recently established for linear reaction-diffusion equations with constant coefficients, an exact solution in the time domain is implicitly derived by means of inverse Laplace transforms. Analytic inverses, whenever they exist, can be obtained in closed form using Mellin transforms. However, highly efficient algorithms are available, and numerical inverses in the time domain are always possible, regardless of the complexity of the Laplace domain expressions. Two illustration tests show that the results coincide well with those of classical exact solutions. Compared to the solutions obtained with series expressions or by numerical methods, closed-form expressions, even in the Laplace domain, represent an innovative alternative and new perspectives can be envisaged. The exact solution via the inverse Laplace transform is shown to be more computationally efficient and thus provides a reference point for numerical and semi-analytical methods.

math.AP↗
arXiv2024

Method of Lie Symmetry for analytical solutions, periodicity and attractivity of a family of tenth-order difference equations

Symmetry is a powerful tool for finding analytical solutions to differential equations, both partial and ordinary, via the similarity variables or via the invariance of the equation under group transformations. It is the largest group of transformations that leaves the differential equation invariant. It is now known that this differential equation method plays the same role when it comes to the study of difference equations. Difference equations can be used to model various phenomena where the changes occur in discrete manner. The use of symmetries on recurrence equations, usually, leads to reductions of order and hence ease the process of finding their solutions. One of the aims of this work is to employ symmetries to generalize some results in the literature. We present new generalized formula solutions of a class of difference equations and we investigate the periodicity and behavior of theses solutions.

math.DS↗
arXiv2023

On a family of higher order recurrence relations: symmetries, formula solutions, periodicity and stability analysis

In this paper, we present formula solutions of a family of difference equations of higher order. We discuss the periodic nature of the solutions and we investigate the stability character of the equilibrium points. We utilize Lie symmetry analysis as part of our approach together with some number theoretic functions. Our findings generalize certain results in the literature.

math.DS↗
arXiv2019

General form of the solutions of some difference equations via Lie symmetry analysis

In this paper, we obtain exact solutions of the following rational difference equation $ x_{n+1}=\frac{x_{n}x_{n-2}x_{n-4}}{ x_{n-1}x_{n-3}(a_{n}+b_{n}x_{n}x_{n-2}x_{n-4})}, $ where $a_{n}$ and $b_{n}$ are random real sequences, by using the technique of Lie symmetry analysis. Moreover, we discuss the periodic nature and behavior of solutions for some special cases. This work is a generalization of some works by Elsayed and Ibrahim in [E.M.Elsayed, T. F. Ibrahim, { Solutions and periodicity of a rational recursive sequences of order five}, Bulletin of the Malaysian Mathematical Sciences Society 38:1 (2015), 95-112].

math.DS↗
arXiv2019

On certain rational recursive sequences of order four

We obtain solutions to the recursive sequences of the form $$x_{n + 1} = \frac{x_{n - 3}x_{n }}{x_{n - 2}(a_n + b_nx_{n -3}x_{n})}$$ where $a_n$ and $b_n$ are arbitrary sequences of real numbers, and the initial values are gives as; $x_{-3},x_{-2}, x_{-1}$ and $x_{0}$. Our methodology is to employ a group theoretic method which lowers the order of the equations, and then solve the resulting lower order recurrence relations that arise therefrom.

math.DS↗
arXiv2016

The Invariance and Conservation Laws of fourth-order Difference Equations

We consider difference equations of order four and determine the one parameter Lie group of transformations (Lie symmetries) that leave them invariant. We introduce a technique for finding their first integrals and discuss the association between the symmetries and first integrals as well as the notion of multipliers (related to conservation laws) for difference equations.

math.CA↗
arXiv2015

Symmetries and Reduction of Discrete Painleve Equations

The construction and role of symmetries for difference equations are now well known. In this paper, the symmetry analysis of the discrete Painleve equations is considered. We assume that the characteristics depend on $n$ and $u_n$ only and we obtain a number of symmetries. These symmetries are used to construct exact solutions in some cases.

math-ph↗