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 automatically.

Comprehensive, timely, and accessible--this is the definitive reference on the application of computerized symbolic...

Partial differential equations (PDEs) play an important role in the natural sciences and technology, because they describe the way systems (natural and other) behave. This book contains the details necessary for the reader to understand the principles and applications of advanced numerical methods for solving PDEs.

This volume contains revised versions of the papers submitted to the workshop by the participants and accepted by the program committee after a thorough reviewing process. The collection of papers included in the proceedings covers not only various expanding applications of computer algebra to scienti?c computing but also the computer algebra systems themselves and the CA algorithms. The eight earlier CASC conferences, CASC 1998, CASC 1999, CASC 2000, CASC 2001, CASC 2002, CASC 2003, CASC 2004, and CASC 2005 were held, - spectively, in St. Petersburg, Russia, in Munich, Germany, in Samarkand,...

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,...

The development of powerful computer algebra systems has considerably ex tended the scope of problems of scientific computing which can now be solved successfully with the aid of computers. However, as the field of applications of computer algebra in scientific computing becomes broader and more complex, there is a danger of separation between theory, systems, and applications. For this reason, we felt the need to bring together the researchers who now ap ply the tools of computer algebra for the solution of problems in scientific computing, in order to foster new and closer interactions....