By Vladimir Dorodnitsyn
Intended for researchers, numerical analysts, and graduate scholars in a number of fields of utilized arithmetic, physics, mechanics, and engineering sciences, Applications of Lie teams to distinction Equations is the 1st publication to supply a scientific building of invariant distinction schemes for nonlinear differential equations. A advisor to tools and leads to a brand new zone of software of Lie teams to distinction equations, distinction meshes (lattices), and distinction functionals, this e-book makes a speciality of the protection of entire symmetry of unique differential equations in numerical schemes. This symmetry renovation ends up in symmetry aid of the variation version in addition to that of the unique partial differential equations and so as relief for usual distinction equations.
A sizeable a part of the ebook is anxious with conservation legislation and primary integrals for distinction versions. The variational procedure and Noether sort theorems for distinction equations are offered within the framework of the Lagrangian and Hamiltonian formalism for distinction equations.
In addition, the ebook develops distinction mesh geometry according to a symmetry crew, simply because diversified symmetries are proven to require varied geometric mesh constructions. the tactic of finite-difference invariants presents the mesh producing equation, any precise case of which promises the mesh invariance. a couple of examples of invariant meshes is gifted. particularly, and with a variety of purposes in numerics for non-stop media, that the majority evolution PDEs must be approximated on relocating meshes.
Based at the built approach to finite-difference invariants, the sensible sections of the publication 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