LEADER 04253nam 22006135 450 001 9910789216003321 005 20210916100500.0 010 $a3-0348-8629-2 024 7 $a10.1007/978-3-0348-8629-1 035 $a(CKB)3400000000101653 035 $a(SSID)ssj0000807667 035 $a(PQKBManifestationID)11492896 035 $a(PQKBTitleCode)TC0000807667 035 $a(PQKBWorkID)10774133 035 $a(PQKB)10433179 035 $a(DE-He213)978-3-0348-8629-1 035 $a(MiAaPQ)EBC3087351 035 $a(PPN)238070972 035 $a(EXLCZ)993400000000101653 100 $a20121227d1992 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aNumerical Methods for Conservation Laws$b[electronic resource] /$fby Randall J. LeVeque 205 $a2nd ed. 1992. 210 1$aBasel :$cBirkhäuser Basel :$cImprint: Birkhäuser,$d1992. 215 $a1 online resource (XII, 220 p. 4 illus.) 225 1 $aLectures in Mathematics. ETH Zürich 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-7643-2723-5 320 $aIncludes bibliographical references. 327 $aI Mathematical Theory -- 1 Introduction -- 2 The Derivation of Conservation Laws -- 3 Scalar Conservation Laws -- 4 Some Scalar Examples -- 5 Some Nonlinear Systems -- 6 Linear Hyperbolic Systems 58 -- 7 Shocks and the Hugoniot Locus -- 8 Rarefaction Waves and Integral Curves -- 9 The Riemann problem for the Euler equations -- II Numerical Methods -- 10 Numerical Methods for Linear Equations -- 11 Computing Discontinuous Solutions -- 12 Conservative Methods for Nonlinear Problems -- 13 Godunov?s Method -- 14 Approximate Riemann Solvers -- 15 Nonlinear Stability -- 16 High Resolution Methods -- 17 Semi-discrete Methods -- 18 Multidimensional Problems. 330 $aThese notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de­ veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un­ derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present­ ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. Without the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are. not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy. 410 0$aLectures in Mathematics. ETH Zürich 606 $aComputer mathematics 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aComputational Mathematics and Numerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M1400X 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 615 0$aComputer mathematics. 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 14$aComputational Mathematics and Numerical Analysis. 615 24$aAnalysis. 676 $a515/.353 686 $a65Mxx$2msc 686 $a35L65$2msc 700 $aLeVeque$b Randall J$4aut$4http://id.loc.gov/vocabulary/relators/aut$042627 906 $aBOOK 912 $a9910789216003321 996 $aNumerical methods for conservation laws$933428 997 $aUNINA