in the present paper the linear oscillator in r3 with z =constanthas been considered. the aim is to determine the necessary conditions forthe persistence of periodic solutions under discontinuous perturbations. a newapproach based on a computational method has been used. at the end weapply our method on an example.

The formulation and the implementation of boundary conditions within the context of the quadrature-free form of the discontinuous Galerkin method are presented for several types of boundary conditions for the Euler equations. An important feature of the discontinuous Galerkin method is that the interior point algorithm is well behaved in the neighborhood of the boundary and requires no modi cat...

In this paper, we develop stability, dissipativity, and optimality notions for dynamical systems with discontinuous vector fields. Specifically, we consider dynamical systems with Lebesgue measurable and locally essentially bounded vector fields characterized by differential inclusions involving Filippov set-valued maps specifying a set of directions for the system velocity and admitting Filipp...

In this paper, we study the superconvergence of the error between the discontinuous Galerkin (DG) finite element solution and the exact solution for linear conservation laws when upwind fluxes are used. We prove that if we apply piecewise k-th degree polynomials, the error between the DG solution and the exact solution is (k+2)-th order superconvergent at the downwind-biased Radau points with s...

In this paper, a discontinuity in beams whose intensity is adjusted by the spring stiffness factor is modeled using a torsional spring. Adapting two analyses in strong and weak forms for discontinuous beams, the improved governing differential equations and the modified stiffness matrix are derived respectively. In the strong form, two different solution methods have been presented to make an a...

In this paper, a discontinuity in beams whose intensity is adjusted by the spring stiffness factor is modeled using a torsional spring. Adapting two analyses in strong and weak forms for discontinuous beams, the improved governing differential equations and the modified stiffness matrix are derived respectively. In the strong form, two different solution methods have been presented to make an a...

This paper generalises the approach taken by Dasgupta & Maskin (1986) and Simon (1989) and provides necessary and su¢ cient conditions for the existence of pure and mixed strategy Nash equilibrium in games with continuous strategy spaces and discontinuous payo¤ functions. The conditions can be applied widely, and examples for existence of pure strategy and monotonic equilibria in First-Price au...

One of the most important issues for Muslim philosophers is the continuous imaginal world and its relationship with the discontinuous imaginative faculty. The continuous imaginal world is a perceptive faculty of the soul known as the faculty of imagination. The discontinuous imaginative faculty is the order of the universe called the imaginal world, which Muslim philosophers have portrayed in a...