in this paper, the reduced dierential transform method is investigated fora nonlinear partial dierential equation modeling nematic liquid crystals, itis called the hunter-saxton equation. the main advantage of this methodis that it can be applied directly to nonlinear dierential equations withoutrequiring linearization, discretization, or perturbation. it is a semi analytical-numerical metho...

Abstract. This paper deals with the formulation of a numerical scheme for solving compressible flow past moving bodies. We use the discontinuos Galerkin finite element method for the space semi-discretization and the Euler backward formula for the time discretization. Moreover, we use ALE mapping for the treatment of a time depended domain and the linearization of inviscid terms using the Vijay...

Conservation properties of a full discretization via a spectral semi-discretization in space and a Lie-Trotter splitting in time for cubic Schrödinger equations with small initial data (or small nonlinearity) are studied. The approximate conservation of the actions of the linear Schrödinger equation, energy, and momentum over long times is shown using modulated Fourier expansions. The results a...

The aim of the present work is to analyze the modified mass method for the dynamic Signorini problem with Coulomb friction. We prove that the space semidiscrete problem is equivalent to an upper semi-continuous one-sided Lipschitz differential inclusion and is, therefore, well-posed. We derive an energy balance. Next, considering an implicit time-integration scheme, we prove that, under a certa...

A new method for the numerical simulation of the so-called soliton dynamics arising in a nonlinear Schrödinger equation in the semi-classical regime is proposed. For the time discretization a classical fourth-order splitting method is used. For the spatial discretization, however, a meshfree method is employed in contrast to the usual choice of (pseudo) spectral methods. This approach allows to...

A general framework for the regularization of constrained PDEs, also called operator DAEs, is presented. The given procedure works for semi-explicit operator DAEs of first order which includes the Navier-Stokes and other flow equations. This reformulation is a regularization in the sense that a semi-discretization in space leads to a DAE of lower index, i.e., of differentiation index 1 instead ...

A one-dimensional free surface problem is considered. It consists in Burgers’ equation with an additional diffusion term on a moving interval. The well-posedness of the problem is investigated and existence and uniqueness results are obtained locally in time. A semi-discretization in space with a piecewise linear finite element method is considered. A priori and a posteriori error estimates are...

In this paper we describe how robot trajectory planning can be formulated as a semi-infinite programming (SIP) problem. The formulation as a SIP problem allowed us to treat the problem with one of the three main classes of methods for solving SIP, the discretization class. Two of the robotics trajectory planning problems formulated were coded in the SIPAMPL [1] environment which is publicly ava...