Applications of Lie Groups to Difference Equations

Bücher

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This book presents a survey of methods and results in a new application area of Lie groups to difference equations and difference meshes (lattices). It focuses on the formulation and mathematical substantiation of exact symmetry preservation in difference models, such as difference equations and meshes. Methods are illustrated with numerous examples and applications in heat and mass transfer, hydrodynamics, physics, and mechanics. To highlight the numerical aspect of the book, the author provides a short survey of methods and theory of finite difference schemes and meshes. He also explains other approaches to quality features of difference schemes, such as variational and moving frames methods.