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Résumé :
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This book is devoted to the numerical approximation of nonlinear hyperbolic systems of conservation laws in one or two space variables. it is intended to be a precise mathematical introduction to the topic. it contains, in particular, a comprehensive treatment of the one-dimensional riemann problem for a hyperbolic system, with special attention to the system of gas dynamics. it offers a complete survey of the usual first-order finite difference schemes for theses systems, including godunov-type, flux-vector splitting and kinetic schemes, with their extension to second-order schemes, and provides a synthesis of recent developments in the field. the book also provides an introduction to multidimensional systems and boundary conditions, both from the theoretical and numerical points of view, presenting in particular the study of finite-volume methods on structured or unstructured meshes.
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