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This book captures the state-of-the-art in the field of Strong Stability Preserving (SSP) time stepping methods, which have significant advantages for the time evolution of partial differential equations describing a wide range of physical phenomena. This comprehensive book describes the development of SSP methods, explains the types of problems which require the use of these methods and demonstrates the efficiency of these methods using a variety of numerical examples. Another valuable feature of this book is that it collects the most useful SSP methods, both explicit and implicit, and presents the other properties of these methods which make them desirable (such as low storage, small error coefficients, large linear stability domains). This book is valuable for both researchers studying the field of time-discretizations for PDEs, and the users of such methods.
Sample Chapter(s)
Chapter 1: Overview: The Development of SSP Methods (153 KB)
Contents:
- Overview: The Development of SSP Methods
- Strong Stability Preserving Explicit Runge–Kutta Methods
- The SSP Coefficient for Runge–Kutta Methods
- SSP Runge–Kutta Methods for Linear Constant Coefficient Problems
- Bounds and Barriers for SSP Runge–Kutta Methods
- Low Storage Optimal Explicit SSP Runge–Kutta Methods
- Optimal Implicit SSP Runge–Kutta Methods
- SSP Properties of Linear Multistep Methods
- SSP Properties of Multistep Multi-Stage Methods
- Downwinding
- Applications
Readership: Computational mathematicians.
“A better model of serious mathematical work written in a warm, reader-friendly style would be very hard to find. A privilege to review, this book has much to offer all numerical analysts, scientists requiring such techniques, and specialists in its field, in addition to making a branch of mathematics more accessible to the wider scientific community. A quality advertisement for mathematics, it can but enhance the status of mathematicians today. This is much more than a mathematical cookbook; it is a state-of-the-art classic in an emerging field.”
“This book provides a very detailed, well written and easily readable study of a class of numerical methods for the solution of ordinary differential equations, the so-called strong stability preserving methods. Special emphasis is placed on the very important question of finding the maximal step size of such methods that can be chosen without destroying the strong stability. Numerous concrete examples of practically important formulas are listed explicitly.”
MathSciNet
“This book provides a very detailed, well written and easily readable study of a class of numerical methods for the solution of ordinary differential equations, the so-called strong stability preserving methods. Special emphasis is placed on the very important question of finding the maximal step size of such methods that can be chosen without destroying the strong stability. Numerous concrete examples of practically important formulas are listed explicitly.”
Zentralblatt MATH
Sample Chapter(s)
Chapter 1: Overview: The Development of SSP Methods (153k)
