Applications of Lie Groups to Difference Equations by Vladimir Dorodnitsyn

By Vladimir Dorodnitsyn

Intended for researchers, numerical analysts, and graduate scholars in a variety of fields of utilized arithmetic, physics, mechanics, and engineering sciences, Applications of Lie teams to distinction Equations is the 1st booklet to supply a scientific development of invariant distinction schemes for nonlinear differential equations. A advisor to equipment and ends up in a brand new zone of program of Lie teams to distinction equations, distinction meshes (lattices), and distinction functionals, this ebook makes a speciality of the protection of whole symmetry of unique differential equations in numerical schemes. This symmetry protection leads to symmetry aid of the variation version in addition to that of the unique partial differential equations and so as aid for usual distinction equations.

A big a part of the e-book is anxious with conservation legislation and primary integrals for distinction types. The variational process and Noether style theorems for distinction equations are provided within the framework of the Lagrangian and Hamiltonian formalism for distinction equations.

In addition, the e-book develops distinction mesh geometry in accordance with a symmetry staff, simply because assorted symmetries are proven to require assorted geometric mesh constructions. the tactic of finite-difference invariants presents the mesh producing equation, any precise case of which promises the mesh invariance. a few examples of invariant meshes is gifted. particularly, and with a number of functions in numerics for non-stop media, that the majority evolution PDEs have to be approximated on relocating meshes.

Based at the built approach to finite-difference invariants, the sensible sections of the booklet 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 recognized equations together with Burgers equation, the KdV equation, and the Schrödinger equation.

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