Numerical Solution of Hyperbolic Partial Differential Equations

A comprehensive graduate textbook on numerical solution of hyperbolic conservation laws. Uniquely combines print and interactive electronic components (on CD).

John A. Trangenstein (Author)

9780521877275, Cambridge University Press

Hardback, published 3 September 2009

620 pages, 109 b/w illus. 2 tables 141 exercises
25.1 x 19.5 x 3.3 cm, 1.5 kg

'Throughout the book it is clear that Trangenstein constantly thinks about students, which is great … could be used as a graduate textbook either independently or as a companion book to other textbooks on the subject. I find it particularly suitable for courses that have an applied flavor.' Doron Levy, University of Maryland

Numerical Solution of Hyperbolic Partial Differential Equations is a new type of graduate textbook, with both print and interactive electronic components (on CD). It is a comprehensive presentation of modern shock-capturing methods, including both finite volume and finite element methods, covering the theory of hyperbolic conservation laws and the theory of the numerical methods. The range of applications is broad enough to engage most engineering disciplines and many areas of applied mathematics. Classical techniques for judging the qualitative performance of the schemes are used to motivate the development of classical higher-order methods. The interactive CD gives access to the computer code used to create all of the text's figures, and lets readers run simulations, choosing their own input parameters; the CD displays the results of the experiments as movies. Consequently, students can gain an appreciation for both the dynamics of the problem application, and the growth of numerical errors.

Preface
1. Introduction to partial differential equations
2. Scalar hyperbolic conservations laws
3. Nonlinear scalar laws
4, Nonlinear hyperbolic systems
5. Methods for scalar laws
6. Methods for hyperbolic systems
7. Methods in multiple dimensions
8. Adaptive mesh refinement
Bibliography
Index.

Subject Areas: Mathematical modelling [PBWH], Numerical analysis [PBKS], Differential calculus & equations [PBKJ]