... materials concerning the subject of this book, the nonlinear stability of nite volume methods for hyperbolic systems of conservation laws, have never been put together and detailed systematically ... (2.23) (2.24) Lemma 2.8 The left-hand side of (2.23) and the right-hand side of (2.24) are nonincreasing functions of r and l respectively In particular, for (2.23) and (2.24) to hold it is necessary ... Conservative schemes Notice that if (2.17) holds for some l , r , then it also holds for l l and r r , because of the convexity of U and of the formulas F (Ul , Ur ) F (Ul ) l l F (Ul , Ur )...