A theoretical framework for the analysis of discontinuous Galerkin approximations of the Maxwell eigenproblem with discontinuous coefficients is presented. Necessary and sufficient conditions for a spurious-free approximation are established, and it is shown that, at least on conformal meshes, basically all the discontinuous Galerkin methods in the literature actually fit into this framework. R...

In this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation$$int_{0}^{1}b(q)D^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$using a fixed point theorem in the Banach algebras. This proof is given in two cases of the continuous and discontinuous function $g$, under the generalized Lipschitz and Caratheodory conditions.

8 Accurate approximations for the derivatives are usually required in many application areas such as biomechanics, chemistry and visualization applications. With the help of Smoothness-Increasing AccuracyConserving (SIAC) filtering, one can enhance the derivatives of a discontinuous Galerkin solution. However, current investigations of derivative filtering are limited to uniform meshes and peri...

Event-driven molecular dynamics simulations are carried out on two rigid-body systems which differ in the symmetry of their molecular mass distributions. First, simulations of methane in which the molecules interact via discontinuous potentials are compared with simulations in which the molecules interact through standard continuous Lennard-Jones potentials. It is shown that under similar condi...

This paper develops least-squares pseudo-spectral collocation methods for elliptic boundary value problems having interface conditions given by discontinuous coefficients and singular source term. From the discontinuities of coefficients and singular source term, we derive the interface conditions and then we impose such interface conditions to solution spaces. We define two types of discrete l...

In this paper, we investigate dynamical behaviors of a large class of delayed differential systems with discontinuous right-hand side. This class of delayed differential systems includes Hopfield and Cellular neural networks with discontinuous activations as special cases. We prove that under some mild conditions, this system has a unique almostperiodic solution, which is globally exponential s...

This paper deals with the boundary value problem involving the differential equation begin{equation*}     ell y:=-y''+qy=lambda y,  end{equation*}  subject to the standard boundary conditions along with the following discontinuity  conditions at a point $ain (0,pi)$  begin{equation*}     y(a+0)=a_1 y(a-0),quad y'(a+0)=a_1^{-1}y'(a-0)+a_2 y(a-0), end{equation*} where $q(x),  a_1 , a_2$ are  rea...