The Kreiss matrix theorem asserts that a family of N X N matrices is L,-stable if and only if either a resolvent condition (R) or a Hennitian norm condition (H) is satisfied. We give a direct, considerahly shorter proof of the power-houndedness of an N X N matrix satisfying (R), sharpening former results by showing that powerhoundedness depends, at most, linearly on the dimension M. We also sho...

A well-known theorem of Lax and Wendroff states that if the sequence of approximate solutions to a system of hyperbolic conservation laws generated by a conservative consistent numerical scheme converges boundedly a.e. as the mesh parameter goes to zero, then the limit is a weak solution of the system. Moreover, if the scheme satisfies a discrete entropy inequality as well, the limit is an entr...

This work introduces a single-stage, single-step method for the compressible Euler equations that is provably positivitypreserving and can be applied on both Cartesian and unstructured meshes. This method is the first case of a singlestage, single-step method that is simultaneously high-order, positivity-preserving, and operates on unstructured meshes. Time-stepping is accomplished via the Lax-...

We present a new algorithm to simulate unsteady viscoelastic flows in abrupt contraction channels. In our approach we split the viscoelastic terms of the Oldroyd-B constitutive equation using Duhamel s formula and discretize the resulting PDEs using a semi-implicit finite difference method based on a Lax–Wendroff method for hyperbolic terms. In particular, we leave a small residual elastic term...

We have developed a new computer program in Fortran 90, in order to obtain numerical solutions of a system of Relativistic Magnetohydrodynamics partial differential equations with predetermined gravitation (GRMHD), capable of simulating the formation of relativistic jets from the accretion disk of matter up to his ejection. Initially we carried out a study on numerical methods of unidimensional...

In many application domains, the preferred approaches to the numerical solution of hyperbolic partial differential equations such as conservation laws are formulated as finite difference schemes. While finite difference schemes are amenable to physical interpretation, one disadvantage of finite difference formulations is that it is relatively difficult to derive the so-called goal oriented a po...

Abstract Conservation properties of iterative methods applied to implicit finite volume discretizations nonlinear conservation laws are analyzed. It is shown that any consistent multistep or Runge-Kutta method globally conservative. Further, it Newton’s method, Krylov subspace and pseudo-time iterations conservative while the Jacobi Gauss-Seidel not in general. If using an explicit a locally di...

In the present work we derive and study a non-linear elliptic PDE coming from the problem of estimation of sound speed inside the Earth. The physical setting of the PDE allows us to pose only a Cauchy problem, and hence is ill-posed. However, we are still able to solve it numerically on a long enough time interval to be of practical use. We used two approaches. The first approach is a finite di...

Many of the recently developed high-resolution schemes for hyperbolic conservation laws are based on upwind di erencing. The building block of these schemes is the averaging of an approximate Godunov solver; its time consuming part involves the eld-byeld decomposition which is required in order to identify the \direction of the wind." Instead, we propose to use as a building block the more robu...