圖書信息
書 名: 守恆定律用的數值法
作 者：（美）勒維克
出版時間： 2010-9-1
ISBN: 9787510027406
開本： 16開
定價: 45.00 元
內容簡介
these notes developed from a course on the numerical solution of conservation laws first taught at the university of washington in the fall of 1988 and then at eth during the following spring.
the overall emphasis is on studying the mathematical tools that are essential in developing, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. a reasonable understanding of the mathematical structure of these equations and their solutions is first required, and part i of these notes deals with this theory. part ii deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. i have stressed the underlying ideas used in various classes of methods rather than presenting the most sophisticated methods in great detail. my aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding.
目錄
ⅰ mathematical theory
1 introduction
1.1 conservation laws
1.2 applications
1.3 mathematical difficulties
1.4 numerical difficulties
1.5 some references
2 the derivation of conservation laws
2.1 integral and differential forms
2.2 scalar equations
2.3 diffusion
3 scalar conservation laws
3.1 the linear advection equation
3.2 burgers' equation
3.3 shock formation
.............
