Numerical Methods for Conservation Laws: From Analysis to Algorithms

Numerical Methods for Conservation Laws: From Analysis to Algorithms is intended for graduate students in computational mathematics and researchers seeking a comprehensive introduction to modern methods for solving conservation laws. Students and researchers in applied sciences and engineering will benefit from the book’s emphasis on algorithmic aspects of complex algorithms.

MATLAB is used to solve examples throughout the book. In addition, a supplemental set of MATLAB code files is available for download.

Features

• Offers the first comprehensive introduction to modern computational methods and their analysis for hyperbolic conservation laws, building on intense research activities for more than four decades of development
• Discusses classic results on monotone and finite difference/finite volume schemes, but emphasizes the successful development of high-order accurate methods for hyperbolic conservation laws
• Addresses modern concepts of TVD and entropy stability, strongly stable Runge-Kutta schemes, and limiter-based methods before discussing essentially non-oscillatory schemes, discontinuous Galerkin methods, and spectral methods
• Explores algorithmic aspects of these methods, emphasizing one- and two-dimensional problems and the development and analysis of an extensive range of methods
• Includes MATLAB code files with which all main methods and computational results in the book can be reproduced
• Demonstrates the performance of many methods on a set of benchmark problems to allow direct comparisons