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Displaying similar documents to “Numerical solution of the Maxwell equations in time-varying media using Magnus expansion”

On the well-balance property of Roe’s method for nonconservative hyperbolic systems. Applications to shallow-water systems

Carlos Parés, Manuel Castro (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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This paper is concerned with the numerical approximations of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The first goal is to introduce a general concept of well-balancing for numerical schemes solving this kind of systems. Once this concept stated, we investigate the well-balance properties of numerical schemes based on the generalized Roe linearizations introduced by [Toumi, J. Comp. Phys. 102 (1992) 360–373]. Next, this general theory is applied to obtain...

A comparison of the accuracy of the finite-difference solution to boundary value problems for the Helmholtz equation obtained by direct and iterative methods

Václav Červ, Karel Segeth (1982)

Aplikace matematiky

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The development of iterative methods for solving linear algebraic equations has brought the question of when the employment of these methods is more advantageous than the use of the direct ones. In the paper, a comparison of the direct and iterative methods is attempted. The methods are applied to solving a certain class of boundary-value problems for elliptic partial differential equations which are used for the numerical modeling of electromagnetic fields in geophysics. The numerical...

An entropy-correction free solver for non-homogeneous shallow water equations

Tomás Chacón Rebollo, Antonio Domínguez Delgado, Enrique D. Fernández Nieto (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this work we introduce an accurate solver for the Shallow Water Equations with source terms. This scheme does not need any kind of entropy correction to avoid instabilities near critical points. The scheme also solves the non-homogeneous case, in such a way that all equilibria are computed at least with second order accuracy. We perform several tests for relevant flows showing the performance of our scheme.