Mathematical Aspects of Numerical Solution of Hyperbolic Systems: 1st Edition (Paperback) book cover

Mathematical Aspects of Numerical Solution of Hyperbolic Systems

1st Edition

By A.G. Kulikovskii, N.V. Pogorelov, A. Yu. Semenov

Chapman and Hall/CRC

560 pages

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Description

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.

Table of Contents

Hyperbolic Systems of Partial Differential Equations. Numerical Solution of Quasi-Linear Hyperbolic Systems. Gas Dynamic Equations. Shallow Water Equations. Magnetohydrodynamic Equations. Solid Dynamics Equation. Nonclassical Discontinuities and Solutions of Hyperbolic Systems.

About the Authors

Kulikovskii, A.G.; Pogorelov, N.V.; Semenov, A. Yu.

About the Series

Monographs and Surveys in Pure and Applied Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations
MAT021000
MATHEMATICS / Number Systems