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AuthorGodlewski, Edwige. author
TitleNumerical Approximation of Hyperbolic Systems of Conservation Laws [electronic resource] / by Edwige Godlewski, Pierre-Arnaud Raviart
ImprintNew York, NY : Springer New York : Imprint: Springer, 1996
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Descript VIII, 510 p. online resource


This work is devoted to the theory and approximation of nonlinear hyperยญ bolic systems of conservation laws in one or two space variables. It follows directly a previous publication on hyperbolic systems of conservation laws by the same authors, and we shall make frequent references to Godlewski and Raviart (1991) (hereafter noted G. R. ), though the present volume can be read independently. This earlier publication, apart from a first chapยญ ter, especially covered the scalar case. Thus, we shall detail here neither the mathematical theory of multidimensional scalar conservation laws nor their approximation in the one-dimensional case by finite-difference conยญ servative schemes, both of which were treated in G. R. , but we shall mostly consider systems. The theory for systems is in fact much more difficult and not at all completed. This explains why we shall mainly concentrate on some theoretical aspects that are needed in the applications, such as the solution of the Riemann problem, with occasional insights into more sophisticated problems. The present book is divided into six chapters, including an introductory chapter. For the reader's convenience, we shall resume in this Introduction the notions that are necessary for a self-sufficient understanding of this book -the main definitions of hyperbolicity, weak solutions, and entropyยญ present the practical examples that will be thoroughly developed in the following chapters, and recall the main results concerning the scalar case


From the contents: Introduction: Definitions and Examples -- Nonlinear hyperbolic systems in one space dimension -- Gas dynamics and reaction flows -- Finite Difference Schemes for one-dimensional systems -- The case of multidimensional systems -- An Introduction to Boundary conditions

Mathematics Numerical analysis Physics Mathematics Numerical Analysis Numerical and Computational Physics Numeric Computing


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