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 thesemethods 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 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...

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