This paper reviews some of the recent developments in upstream difference schemes
through a unified representation, in order to enable comparison between the various …

Publisher Summary This chapter focuses on finite volume methods. The finite volume
method is a discretization method that is well suited for the numerical simulation of various …

These notes developed from a course on the numerical solution of conservation laws first
taught at the University of Washington in the fall of 1988 and then at ETH during the …

A class of new explicit second order accurate finite difference schemes for the computation
of weak solutions of hyperbolic conservation laws is presented. These highly nonlinear …

An adaptive method based on the idea of multiple component grids for the solution of
hyperbolic partial differential equations using finite difference techniques is presented …

The technique of obtaining high resolution, second order, oscillation free (TVD), explicit
scalar difference schemes, by the addition of a limited antidiffusive flux to a first order …

I am extremely gratified by the wide acceptance of the first edition of this textbook. It confirms
that there was a need for a textbook to cover the basic theory of finite difference schemes for …

In these lecture notes we describe the construction, analysis, and application of ENO
(Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

In this paper, we review the development of the Runge–Kutta discontinuous Galerkin
(RKDG) methods for non-linear convection-dominated problems. These robust and accurate …