in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

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 analytical and numerical solutions to the Dirichlet boundary value problem for the biharmonic partial differential equation, on a disk of finite radius in the plane. The physical interpretation of these solutions is that of the harmonic oscillations of a thin, clamped plate. For the linear, fourth-order, biharmonic partial differential equation in the plane, it is well...

We study a non-ergodic transition in a many-body Langevin system. We first derive an equation for the two-point time correlation function of density fluctuations, ignoring the contributions of the thirdand fourth-order cummulants. For this equation, with the average density fixed, we find that there is a critical temperature at which the qualitative nature of the trajectories around the trivial...

We show that the local equivalence problem of second-order ordinary differential equations under point transformations is completely characterized by differential invariants of order at most 10 and that this upper bound is sharp. We also demonstrate that, modulo Cartan duality and point transformations, the Painlevé–I equation can be characterized as the simplest second-order ordinary different...

In atmospheric dynamics, the governing equations are usually non-linear partial differential equations. Some knowledge of finite-difference approximations to ordinary differential equations (especially first order) is needed, however. In fact, if we linearize a governing partial differential equation and assume a wave form for the solution, the equation simply reduces to an ordinary differentia...

We study the linearization of a class of Liénard type nonlinear second-order ordinary differential equations from the generalized Sundman transformation viewpoint. The linearizing generalized Sundman transformation for the class of equations is constructed. The transformation is used to map the underlying class of equations into a linear second-order ordinary differential equation which is not ...

a new two-step implicit linear obrechkoff twelfth algebraic order method with vanished phase-lag and its first, second, third and fourth derivatives is constructed in this paper. the purpose of this paper is to develop an efficient algorithm for the approximate solution of the one-dimensional radial schrodinger equation and related problems. this algorithm belongs in the category of the multist...