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Numerical Methods for Conservation Laws

  • Randall J. LeVeque

Table of contents

  1. Front Matter
    Pages i-viii
  2. Mathematical Theory

    1. Front Matter
      Pages ix-ix
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      Pages 1-13
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      Pages 14-18
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      Pages 19-40
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      Pages 41-50
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      Pages 70-80
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      Pages 81-88
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      Pages 89-93
  3. Numerical Methods

    1. Front Matter
      Pages 95-95
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      Pages 97-113
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  4. Back Matter
    Pages 208-214

About this book

Introduction

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 following spring. The overall emphasis is on studying the mathematical tools that are essential in de­ veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un­ derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present­ ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. vVithout the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy.

Keywords

numerical method research shock wave university

Authors and affiliations

  • Randall J. LeVeque
    • 1
  1. 1.Department of Mathematics, GN-50University of WashingtonSeattleUSA

Bibliographic information