Provably stable flux reconstruction (FR) schemes are derived for partial differential equations cast in curvilinear coordinates. Specifically, energy (ESFR) considered as they allow design flexibility well stability proofs the linear advection problem on affine elements. Additionally, split forms examined enable development of proofs. The first critical step proves, that coordinates, discontinu...

In this work, we focus on the numerical approximation of a hybrid fluid-kinetic plasma model for electrons, in which energetic electrons are described by Vlasov kinetic whereas fluid is used cold population electrons. First, study validity modeling two dimensional context (one dimension space and one velocity) against full (stiff) second, four configuration considered three dimensions following...

One of the famous third-order iterative methods for finding simultaneously all zeros a polynomial was introduced by Ehrlich in 1967. In this paper, we construct new family high-order as combination Ehrlich’s iteration function and an arbitrary function. We call these with correction. The paper provides detailed local convergence analysis presented large class functions. As consequence, obtain t...

In this paper, we investigate the stability of a numerical method for solving wave equation. The uses explicit leap-frog in time and high order continuous discontinuous (DG) finite elements using standard Lagrange Hermite basis functions space. Matrix eigenvalue analysis is used to calculate time-step restrictions. We show that restriction independent nodal distribution, such as equidistributed...