Victor G. Ganzha - Böcker

Advances in computer technology have conveniently coincided withtrends in numerical analysis toward increased complexity ofcomputational algorithms based on finite difference methods. It isno longer feasible to perform stability investigation of thesemethods manually--and no longer necessary. As this book shows,modern computer algebra tools can be combined with methods fromnumerical analysis to generate programs that will do the jobautomatically. Comprehensive, timely, and accessible--this is the definitivereference on the application of computerized symbolic manipulationsfor analyzing the stability of a wide range of difference schemes.In particular, it deals with those schemes that are used to solvecomplex physical problems in areas such as gas dynamics, heat andmass transfer, catastrophe theory, elasticity, shallow watertheory, and more. Introducing many new applications, methods, and concepts,Computer-Aided Analysis of Difference Schemes for PartialDifferential Equations* Shows how computational algebra expedites the task of stabilityanalysis--whatever the approach to stability investigation* Covers ten different approaches for each stability method* Deals with the specific characteristics of each method and itsapplication to problems commonly encountered by numerical modelers* Describes all basic mathematical formulas that are necessary toimplement each algorithm* Provides each formula in several global algebraic symboliclanguages, such as MAPLE, MATHEMATICA, and REDUCE* Includes numerous illustrations and thought-provoking examplesthroughout the text For mathematicians, physicists, and engineers, as well as forpostgraduate students, and for anyone involved with numericsolutions for real-world physical problems, this book provides avaluable resource, a helpful guide, and a head start ondevelopments for the twenty-first century.

CASC 2005 continued a tradition - started in 1998 - of international c- ferences on the latest advances in the application of computer algebra systems (CASs) and methods to the solution of various problems in scienti?c computing. The methods of scienti?c computing play an important role in research and engineering applications in the natural and the engineering sciences. The sign- icance and impact of computer algebra methods and computer algebra systems for scienti?c computing has increased considerably in recent times. Nowadays, suchgeneral-purposecomputeralgebrasystemsasMaple,Magma,Mathematica, MuPAD, Singular, CoCoA and others enable their users to solve the following three important tasks within a uniform framework: (a) symbolic manipulation; (b) numerical computation; (c) visualization. The ongoing development of such systems, including their integrationand ad- tation to modern software environments, puts them at the forefront in scienti?c computing and enables the practicalsolution of many complex applied problems in the domains of natural sciences and engineering. Greece o?ers excellent infrastructures for hosting international conferences, and this was a reason for us to choose the city of Kalamata, Greece, as the lo- tion for CASC 2005,the eighth conference in the sequenceof CASC conferences.The seven earlier CASC conferences, CASC 1998, CASC 1999, CASC 2000, CASC 2001, CASC 2002, CASC 2003, and CASC 2004 were held, respectively, in St. Petersburg, Russia, in Munich, Germany, in Samarkand, Uzbekistan, in Konstanz, Germany, in the Crimea (Ukraine), in Passau (Germany), and in St. Petersburg, Russia, and they proved to be successful.