Differential matrix models provide an elementary blueprint for the adequate and efficient treatment of many important applications in science engineering. In present work, we suggest a procedure, extending our previous research results, to represent solutions nonlinear differential problems fourth order given form Y(4)(x)=f(x,Y(x)) terms higher-order splines. The corresponding algorithm is expl...

For a class of fourth order gradient flow problems, integration the scalar auxiliary variable (SAV) time discretization with penalty-free discontinuous Galerkin (DG) spatial leads to SAV-DG schemes. These schemes are linear and shown unconditionally energy stable. However, reduced systems rather expensive solve due dense coefficient matrices. In this paper, we provide procedure pre-evaluate in ...

Abstract. In this paper we investigate symmetry-preserving boundary conditions for a fourth-order symmetry-preserving finite volume method, to able to do accurate turbulence simulations for wind-turbine wake applications. It is found that the use of Dirichlet conditions limits the fourth-order method to (at most) second order. However, on properly chosen non-uniform grids, fourth-order behavior...

In this paper, we present and analyse fourth order method for finding simultaneously multiple zeros of polynomial equations. S. M. Ilič and L. Rančič modified cubically convergent Ehrlich Aberth method to fourth order for the simultaneous determination of simple zeros [5]. We generalize this method to the case of multiple zeros of complex polynomial equations. It is proved that the method has f...

A fourth-order numerical method for the zero-Mach-number limit of the equations for compressible flow is presented. The method is formed by discretizing a new auxiliary variable formulation of the conservation equations, which is a variable density analog to the impulse or gauge formulation of the incompressible Euler equations. An auxiliary variable projection method is applied to this formula...

In this paper we make a comparison between the two-scale asymptotic expansion method for periodic homogenization and the so-called Bloch wave method. It is wellknown that the homogenized tensor coincides with the Hessian matrix of the first Bloch eigenvalue when the Bloch parameter vanishes. In the context of the two-scale asymptotic expansion method, there is the notion of high order homogeniz...

Using the Dirac constraint method we show that the pure fourth-order PaisUhlenbeck oscillator model is free of observable negative norm states. Even though such ghosts do appear when the fourth order theory is coupled to a second order one, the limit in which the second order action is switched off is found to be a highly singular one in which these states move off shell. Given this result, con...