By Vladimir Dorodnitsyn
Intended for researchers, numerical analysts, and graduate scholars in numerous fields of utilized arithmetic, physics, mechanics, and engineering sciences, Applications of Lie teams to distinction Equations is the 1st booklet to supply a scientific building of invariant distinction schemes for nonlinear differential equations. A consultant to equipment and leads to a brand new sector of software of Lie teams to distinction equations, distinction meshes (lattices), and distinction functionals, this ebook makes a speciality of the upkeep of entire symmetry of unique differential equations in numerical schemes. This symmetry upkeep leads to symmetry aid of the variation version in addition to that of the unique partial differential equations and so as aid for traditional distinction equations.
A immense a part of the publication is anxious with conservation legislation and primary integrals for distinction types. The variational procedure and Noether kind theorems for distinction equations are offered within the framework of the Lagrangian and Hamiltonian formalism for distinction equations.
In addition, the booklet develops distinction mesh geometry in accordance with a symmetry crew, simply because diverse symmetries are proven to require various geometric mesh constructions. the strategy of finite-difference invariants presents the mesh producing equation, any distinctive case of which promises the mesh invariance. a couple of examples of invariant meshes is gifted. particularly, and with a variety of functions in numerics for non-stop media, that the majority evolution PDEs have to be approximated on relocating meshes.
Based at the constructed approach to finite-difference invariants, the sensible sections of the ebook current dozens of examples of invariant schemes and meshes for physics and mechanics. specifically, there are new examples of invariant schemes for second-order ODEs, for the linear and nonlinear warmth equation with a resource, and for famous equations together with Burgers equation, the KdV equation, and the Schrödinger equation.
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Applications of Lie Groups to Difference Equations (Differential and Integral Equations and Their Applications) by Vladimir Dorodnitsyn