Since the appearance of computers, numerical methods for discontinuous solutions of quasi-linear hyperbolic systems of partial differential equations have been among the most important research subjects in numerical analysis. The authors have developed a new difference method (named the singularity-separating method) for quasi-linear hyperbolic systems of partial differential equations. Its most important feature is that it possesses a high accuracy even for problems with singularities such as schocks, contact discontinuities, rarefaction waves and detonations. Besides the thorough description of the method itself, its mathematical foundation (stability-convergence theory of difference schemes for initial-boundary-value hyperbolic problems) and its application to supersonic flow around bodies are discussed. Further, the method of lines and its application to blunt body problems and conical flow problems are described in detail. This book should soon be an important working basis for both graduate students and researchers in the field of partial differential equations as well as in mathematical physics.

Contenuti:

I Numerical Methods.- 1 Numerical Methods for Initial-Boundary-Value Problems for First Order Quasilinear Hyperbolic Systems in Two Independent Variables.- 2 Numerical Methods for a Certain Class of Initial-Boundary-Value Problems for the First Order Quasilinear Hyperbolic Systems in Three Independent Variables.- 3 Numerical Schemes for Certain Boundary-Value Problems of Mixed-Type and Elliptical Equations.- II Inviscid Supersonic Flow Around Bodies.- 4 Inviscid Steady Flow.- 5 Calculation of Supersonic Flow around Blunt Bodies.- 6 Calculation of Supersonic Conical Flow.- 7 Solution of Supersonic Regions of Flow around Combined Bodies.- References.- General References.- Special References A: Numerical Calculation of Flow in Subsonic and Transonic Regions.- Special References B: Numerical Calculation of Conical Flow.- Special References C: Numerical Calculation of Flow in Supersonic Regions.

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