in this paper, a chebyshev finite difference method has been proposed in order to solvenonlinear two-point boundary value problems for second order nonlinear differentialequations. a problem arising from chemical reactor theory is then considered. the approachconsists of reducing the problem to a set of algebraic equations. this method can be regardedas a non-uniform finite difference scheme. t...

consider the linear system ax=b where the coefficient matrix a is an m-matrix. in the present work, it is proved that the rate of convergence of the gauss-seidel method is faster than the mixed-type splitting and aor (sor) iterative methods for solving m-matrix linear systems. furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a precondition...

consider the linear system ax=b where the coefficient matrix a is an m-matrix. in the present work, it is proved that the rate of convergence of the gauss-seidel method is faster than the mixed-type splitting and aor (sor) iterative methods for solving m-matrix linear systems. furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a precondition...

We consider a Newton-Krylov approach for discretized compressible Euler equations. A good preconditioner in the Krylov subspace method is essential for obtaining an efficient solver in such an approach. In this paper we compare point-block-Gauss-Seidel, point-block-ILU and point-block-SPAI preconditioners. It turns out that the SPAI method is not satisfactory for our problem class. The point-bl...

Here is a proof for the demeaning method used in lfe, and a description of the methods used for solving the residual equations. As well as a toy-example. This is a preliminary version of [3]. This method, formulated as the Gauss-Seidel algorithm, was noted in [4] without the author noticing it in the first version of this paper.

The q-deformed commutation relation aa ? qa a = 1 1 for the harmonic os-cillator is considered with q 2 ?1; 1]. An explicit representation generalizing the Bargmann representation of analytic functions on the complex plane is constructed. In this representation the distribution of a + a in the vacuum state is explicitly calculated. This distribution is to be regarded as the natural q-deformatio...

The multigrid method for discontinuous Galerkin discretizations of advection-diffusion problems is presented. It is based on a block Gauss-Seidel smoother with downwind ordering honoring the advection operator. The cell matrices of the DG scheme are inverted in this smoother in order to obtain robustness for higher order elements. Employing a set of experiments, we show that this technique actu...

The objective of this paper is to construct and investigate smooth orientable surfaces in RN −1 by analytical methods. The structural equations of surfaces in connection with CPN−1 sigma models on Minkowski spacetime are studied in detail. This is carried out using a moving frame adapted to the surface immersed in su(N) algebra. The first and second fundamental forms of the surface as well as t...

Introduction In this paper we present a modification of Gauss-Huard's method for solving dense linear systems that allows an efficient implementation on machines with a hierarchical memory structure. GaussHuard's method resembles Gauss-Jordan's method in the fact that it reduces the given system by elementary transformations to a diagonal system and it resembles regular Gaussian elimination in ...