In this paper we study the two-dimensional version of the RungeKutta Local Projection Discontinuous Galerkin (RKDG) methods, already defined and analyzed in the one-dimensional case. These schemes are defined on general triangulations. They can easily handle the boundary conditions, verify maximum principles, and are formally uniformly high-order accurate. Preliminary numerical results showing ...

We study semi-Lagrangian discontinuous Galerkin (SLDG) and RungeKutta discontinuous Galerkin (RKDG) schemes for some front propagation problems in the presence of an obstacle term, modeled by a nonlinear Hamilton-Jacobi equation of the form min(ut+cux, u−g(x)) = 0, in one space dimension. New convergence results and error bounds are obtained for Lipschitz regular data. These “low regularity” as...

The scope of this paper is to present, both from a theoretical and a practical viewpoint, the problem of the thermal boundary-layer approximation for free convection flow in a porous medium bounded by a vertical flat plate (wall). The influence of the wall temperature and heat flux on the problem solution is discussed. We present numerical results for the problem of steady free convection using...

----------------------------------------------------ABSTRACT-----------------------------------------------------In the present paper is an investigation of heat and mass transfer characteristics of MHD free convection of steady flow of an incompressible electrically conducting fluid over an inclined plate under the influence of an applied uniform magnetic field and the effects of Hall current ...

Differential equations arise in mathematics, physics, medicine, pharmacology, communications, image processing and animation, etc. An Ordinary Differential Equation (ODE) is a differential equation if it involves derivatives with respect to only one independent variable which can be studied from different perspectives; such as: analytical methods, graphical methods and numerical methods. This r...

The main purpose of the paper is to show how to use implicit-explicit (IMEX) RungeKutta methods in a much more general context than usually found in the literature, obtaining very effective schemes for a large class of problems. This approach gives a great flexibility, and allows, in many cases the construction of simple linearly implicit schemes without any Newton’s iteration. This is obtained...

In this paper, we study a finite capacity Markovian multi-server queuing system with discouraged arrivals, reneging, and retention of reneging customers. The transient state probabilities of the queuing system are obtained by using a computational technique based on the 4th order RungeKutta method. With the help of the transient state probabilities, we develop some important measures of perform...

A water surface slope limiting scheme is tested and compared with the water depth slope limiter for the solution of one dimensional shallow water equations with bottom slope source term. Numerical schemes based on the total variation diminishing RungeKutta discontinuous Galerkin finite element method with slope limiter schemes based on water surface slope and water depth are used to solve one-d...

The numerical efficiency of different schemes for solving the Liouvillevon Neumann equation within multilevel Redfield theory has been studied. Among the tested algorithms are the well-known Runge-Kutta scheme in two different implementations as well as methods especially developed for time propagation: the Short Iterative Arnoldi, Chebyshev and Newtonian propagators. In addition, an implementa...

Abstract. This paper presents a characteristic-based flux partitioning for the semi-implicit time integration of atmospheric flows. Nonhydrostatic models require the solution of the compressible Euler equations. The acoustic time-scale is significantly faster than the advective scale, yet it is typically not relevant to atmospheric and weather phenomena. The acoustic and advective components of...