Download E-books Applications of Lie Groups to Difference Equations (Differential and Integral Equations and Their Applications, Volume 8) PDF
By Vladimir Dorodnitsyn
Meant for researchers, numerical analysts, and graduate scholars in quite a few fields of utilized arithmetic, physics, mechanics, and engineering sciences, functions of Lie teams to distinction Equations is the 1st ebook to supply a scientific development of invariant distinction schemes for nonlinear differential equations. A advisor to tools and leads to a brand new sector of software of Lie teams to distinction equations, distinction meshes (lattices), and distinction functionals, this e-book specializes in the protection of whole symmetry of unique differential equations in numerical schemes. This symmetry maintenance ends up in 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 considerable a part of the e-book is worried with conservation legislation and primary integrals for distinction versions. The variational technique and Noether kind theorems for distinction equations are offered within the framework of the Lagrangian and Hamiltonian formalism for distinction equations. furthermore, the ebook develops distinction mesh geometry according to a symmetry crew, simply because various symmetries are proven to require diversified geometric mesh buildings. the tactic of finite-difference invariants presents the mesh producing equation, any detailed case of which promises the mesh invariance. a few examples of invariant meshes is gifted. specifically, and with a variety of purposes in numerics for non-stop media, that almost all evolution PDEs must be approximated on relocating meshes. in accordance with the built approach to finite-difference invariants, the sensible sections of the e-book current dozens of examples of invariant schemes and meshes for physics and mechanics. particularly, 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 Schr?dinger equation.