NUMERICAL SOLUTION OF HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS

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文件名称：NUMERICAL SOLUTION OF HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS
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更新时间：2013-04-29 17:10:08
hyperbolic PDE 关于双曲型方程剑桥经典书籍！好东西分享！ Hyperbolic conservation laws describe a number of interesting physical problems in diverse areas such as fluid dynamics, solid mechanics, and astrophysics. Our emphasis in this book is on nonlinearities in these problems, especially those that lead to the development of propagating discontinuities. These propagating discontinuities can appear as the familiar shockwaves in gases (the “boom” from explosions or super-sonic airplanes), but share many mathematical properties with other waves that do not appear to be so “shocking” (such as steep changes in oil saturations in petroleum reservoirs). These nonlinearities require special treatment, usually by methods that are themselves nonlinear. Of course, the numerical methods in this book can be used to solve linear hyperbolic conservation laws, but our methods will not be as fast or accurate as possible for these problems. If you are only interested in linear hyperbolic conservation laws, you should read about spectral methods and multipole expansions.