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This guide presents methods and results in a new area of application of Lie groups to difference equations, difference meshes (lattices), and difference functional. It is perhaps the first book to provide a systematic construction of invariant difference schemes for nonlinear differential equations. It focuses on the preservation of complete symmetry of original differential equations in numerical schemes. A substantial part of the text is concerned with conservation laws and first integrals for difference models. The book also includes dozens of examples of invariant schemes and meshes for physics and mechanics.
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