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Mathematical Aspects of Numerical Solution of Hyperbolic Systems (Paperback)
Loot Price: R1,937
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Mathematical Aspects of Numerical Solution of Hyperbolic Systems (Paperback)
Series: Monographs and Surveys in Pure and Applied Mathematics
Expected to ship within 12 - 17 working days
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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.
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