In this paper we study conservation laws with spatially-varying flux functions. We give a survey of some schemes (based on finite volume methods) to solve non-autonomous conservation laws of the form . Numerical experiments are presented.
This paper concerns -velocity model of the general linear time-dependent transport equation. The assumed probability of the collision (scattering, fission) depends only on the angle of the directions of the moving neutron before and after the collision. The weak formulation of the problem is given and a priori estimates are obtained. The construction of an approximate problem by -method is given. In the symmetric hyperbolic system obtained by -method dissipativity and -orthogonality of the relevant...
In this paper we analyse an algorithm which is a modification of the so-called two-level algorithm with overcorrection, published in [2]. We illustrate the efficiency of this algorithm by a model example.
A two-level algebraic algorithm is introduced and its convergence is proved. The restriction as well as prolongation operators are defined with the help of aggregation classes. Moreover, a particular smoothing operator is defined in an analogical way to accelarate the convergence of the algorithm. A model example is presented in conclusion.
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