The concepts of stability regions, Aand A(α)-stability – albeit based on scalar models – turned out to be essential for the identification of implicit methods suitable for the integration of stiff ODEs. However, for multistep methods, knowledge of the stability region provides no information on the quantitative stability behavior of the scheme. In this paper we fill this gap for the important c...

In this talk we consider the numerical difficulties that arise when horizontal advection is coupled with chemistry on a sphere, using operator splitting. From a numerical point of view, these two processes are the most difficult parts of an atmospheric model for global studies. The advection process is solved on a uniform grid and on a so-called reduced grid, where less cells are used near the ...

In this paper, we extend a previous work on a compact scheme for the steady Navier Stokes equations [Li, Tang, and Fornberg (1995), Int. J. Numer. Methods Fluids, 20, 1137 1151] to the unsteady case. By exploiting the coupling relation between the streamfunction and vorticity equations, the Navier Stokes equations are discretized in space within a 3_3 stencil such that a fourth order accuracy i...

Robust and accurate schemes are designed to simulate the coupling between subsurface and overland flows. The coupling conditions at the interface enforce the continuity of both the normal flux and the pressure. Richards’ equation governing the subsurface flow is discretized using a Backward Differentiation Formula and a symmetric interior penalty Discontinuous Galerkin method. The kinematic wav...

Implicit-explicit (IMEX) multistep methods are very useful for the time discretiza-tion of convection diffusion PDE problems such as the Burgers equations and also the incompressible Navier-Stokes equations. Semi-discretization in space of the latter typically gives rise to an index 2 differential-algebraic (DAE) system of equations. Runge-Kutta (RK) methods have been considered for the time di...

In this paper, we present a numerical method for solving nonlinear differential algebraic equations (DAE’s) based on the backward differential formulas (BDF) and the Pade series. Usefulness of the method is then illustrated by a numerical example, which is concerned with the derivation of the optimal guidance law for spacecraft. This kind of problems is called trajectory-prescribed path control...

A study is presented on the topic of numerical efficiency of TD-FEM with the use of BDF. The BDF coefficients are calculated with the use of Lagrange polynomials. The paper also presents two strategies of time-step adaptation. The obtained numerical solutions have been compared with analytical solutions of the selected problems in order to check their accuracy. Streszczenie. Przedstawiono badan...

We deduce the structure of the Dirac field on the lattice from the discrete version of differential geometry and from the representation of the integral Lorentz transformations. The analysis of the induced representations of the Poincaré group on the lattice reveals that they are reducible, a result that can be considered a group theoretical approach to the problem of fermion doubling. 1. DISCR...

A simple Gauss-Seidel technique is proposed which exploits the special form of the chemical kinetics equations. Classical Aitken extrapolation is applied to accelerate convergence. The technique is meant for implementation in stii solvers that are used in long range transport air pollution codes using operator splitting. Splitting necessarily gives rise to a great deal of integration restarts. ...

This paper considers the gas phase chemistry in a protoplanetary accretion disk, especially the chemistry initiated in the gas phase by destruction of dust close to the central star. Slow radial particle transport moves gas and dust from the cold outer parts of a protoplanetary accretion disk into its warm central part where chemical reactions in the gas phase are activated. At the same time ga...