Advances in computer technology have conveniently coincided with
trends in numerical analysis toward increased complexity of
computational algorithms based on finite difference methods. It is
no longer feasible to perform stability investigation of these
methods manually--and no longer necessary. As this book shows,
modern computer algebra tools can be combined with methods from
numerical analysis to generate programs that will do the job
Comprehensive, timely, and accessible--this is the definitive
reference on the application of computerized symbolic manipulations
for analyzing the stability of a wide range of difference schemes.
In particular, it deals with those schemes that are used to solve
complex physical problems in areas such as gas dynamics, heat and
mass transfer, catastrophe theory, elasticity, shallow water
theory, and more.
Introducing many new applications, methods, and concepts,
Computer-Aided Analysis of Difference Schemes for Partial
* Shows how computational algebra expedites the task of stability
analysis--whatever the approach to stability investigation
* Covers ten different approaches for each stability method
* Deals with the specific characteristics of each method and its
application to problems commonly encountered by numerical modelers
* Describes all basic mathematical formulas that are necessary to
implement each algorithm
* Provides each formula in several global algebraic symbolic
languages, such as MAPLE, MATHEMATICA, and REDUCE
* Includes numerous illustrations and thought-provoking examples
throughout the text
For mathematicians, physicists, and engineers, as well as for
postgraduate students, and for anyone involved with numeric
solutions for real-world physical problems, this book provides a
valuable resource, a helpful guide, and a head start on
developments for the twenty-first century.
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