‎in this paper‎, ‎we introduce $alpha$-$psi$-contractive mapping in partially ordered sets and construct fixed point theorems to solve a first-order ordinary differential equation by existence of its lower solution.

‎this paper obtains the exact solutions of the wave equation as a second-order partial differential equation (pde)‎. ‎we are going to calculate polynomial and non-polynomial exact solutions by using lie point symmetry‎. ‎we demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎a generalized procedure for polynomial solution is pr...

The Fuchsian differential equation is a linear differential equation whose singularities are all regular. It frequently appears in a range of problems in mathematics and physics. For example, the famous Gauss hypergeometric differential equation is a canonical form of the second-order Fuchsian differential equation with three singularities on the Riemann sphere C ∪ {∞}. Global properties of sol...

‎in this paper, we formulate the fourth order sturm-liouville problem (fslp) as a lie group matrix differential equation. by solving this ma- trix differential equation by lie group magnus expansion, we compute the eigenvalues of the fslp. the magnus expansion is an infinite series of multiple integrals of lie brackets. the approximation is, in fact, the truncation of magnus expansion and a gauss...

This survey paper reports on the properties of the fourth-order Bessel-type linear ordinary differential equation, on the generated self-adjoint differential operators in two associated Hilbert function spaces, and on the generalisation of the classical Hankel integral transform. These results are based upon the properties of the classical Bessel and Laguerre second-order differential equations...

‎semidiscrete finite element approximation of a hyperbolic type‎ ‎integro-differential equation is studied. the model problem is‎ ‎treated as the wave equation which is perturbed with a memory term.‎ ‎stability estimates are obtained for a slightly more general problem.‎ ‎these, based on energy method, are used to prove optimal order‎ ‎a priori error estimates.‎

in this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. a fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. thomas algorithm is used to solve the tri-diagonal system. the stability of the algorithm is investigated. it ...

In this paper, we consider First-order fuzzy differential equations with initial value conditions. The convergence, consistency and stability of difference method for approximating the solution of fuzzy differential equations involving generalized H-differentiability, are studied. Then the local truncation error is defined and sufficient conditions for convergence, consistency and stability of ...

In this paper, an inverse nodal problem for a second-order differential equation having a chemical potential on a finite interval is investigated. First, we estimate the nodal points and nodal lengths of differential operator. Then, we show that the potential can be uniquely determined by a dense set of nodes of the eigenfunctions.

nonlinear difference equations of higher order are important in applications; such equations appear naturally as discrete analogues of differential and delay differential equations which model various diverse phenomena in biology, ecology, economics, physics and engineering. the study of dynamical properties of such equations is of great importance in many areas. the autonomous difference equat...