Mathematical Aspects of Numerical Solution of Hyperbolic Systems

Mathematical Aspects of Numerical Solution of Hyperbolic Systems
Author :
Publisher : CRC Press
Total Pages : 564
Release :
ISBN-10 : 0849306086
ISBN-13 : 9780849306082
Rating : 4/5 (082 Downloads)

Book Synopsis Mathematical Aspects of Numerical Solution of Hyperbolic Systems by : A.G. Kulikovskii

Download or read book Mathematical Aspects of Numerical Solution of Hyperbolic Systems written by A.G. Kulikovskii and published by CRC Press. This book was released on 2000-12-21 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. The authors present the material in the context of the important mechanical applications of such systems, including the Euler equations of gas dynamics, magnetohydrodynamics (MHD), shallow water, and solid dynamics equations. This treatment provides-for the first time in book form-a collection of recipes for applying higher-order non-oscillatory shock-capturing schemes to MHD modelling of physical phenomena. The authors also address a number of original "nonclassical" problems, such as shock wave propagation in rods and composite materials, ionization fronts in plasma, and electromagnetic shock waves in magnets. They show that if a small-scale, higher-order mathematical model results in oscillations of the discontinuity structure, the variety of admissible discontinuities can exhibit disperse behavior, including some with additional boundary conditions that do not follow from the hyperbolic conservation laws. Nonclassical problems are accompanied by a multiple nonuniqueness of solutions. The authors formulate several selection rules, which in some cases easily allow a correct, physically realizable choice. This work systematizes methods for overcoming the difficulties inherent in the solution of hyperbolic systems. Its unique focus on applications, both traditional and new, makes Mathematical Aspects of Numerical Solution of Hyperbolic Systems particularly valuable not only to those interested the development of numerical methods, but to physicists and engineers who strive to solve increasingly complicated nonlinear equations.


Mathematical Aspects of Numerical Solution of Hyperbolic Systems Related Books

Mathematical Aspects of Numerical Solution of Hyperbolic Systems
Language: en
Pages: 564
Authors: A.G. Kulikovskii
Categories: Mathematics
Type: BOOK - Published: 2000-12-21 - Publisher: CRC Press

GET EBOOK

This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic syste
Mathematical Aspects of Numerical Solution of Hyperbolic Systems
Language: en
Pages: 555
Authors: A.G. Kulikovskii
Categories: Mathematics
Type: BOOK - Published: 2000-12-21 - Publisher: CRC Press

GET EBOOK

This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic syste
Numerical Approximation of Hyperbolic Systems of Conservation Laws
Language: en
Pages: 846
Authors: Edwige Godlewski
Categories: Mathematics
Type: BOOK - Published: 2021-08-28 - Publisher: Springer Nature

GET EBOOK

This monograph is devoted to the theory and approximation by finite volume methods of nonlinear hyperbolic systems of conservation laws in one or two space vari
Finite Volume Methods for Hyperbolic Problems
Language: en
Pages: 582
Authors: Randall J. LeVeque
Categories: Mathematics
Type: BOOK - Published: 2002-08-26 - Publisher: Cambridge University Press

GET EBOOK

This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approxim
Hyperbolic Problems: Theory, Numerics, Applications
Language: en
Pages: 514
Authors: Michael Fey
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Birkhäuser

GET EBOOK

[Infotext]((Kurztext))These are the proceedings of the 7th International Conference on Hyperbolic Problems, held in Zürich in February 1998. The speakers and c