By Vladimir Dorodnitsyn
Intended for researchers, numerical analysts, and graduate scholars in quite a few fields of utilized arithmetic, physics, mechanics, and engineering sciences, Applications of Lie teams to distinction Equations is the 1st ebook to supply a scientific building of invariant distinction schemes for nonlinear differential equations. A consultant to tools and leads to a brand new region of program of Lie teams to distinction equations, distinction meshes (lattices), and distinction functionals, this e-book makes a speciality of the protection of whole symmetry of unique differential equations in numerical schemes. This symmetry upkeep leads to symmetry relief of the variation version in addition to that of the unique partial differential equations and so as relief for usual distinction equations.
A enormous a part of the booklet is worried with conservation legislation and primary integrals for distinction types. The variational procedure and Noether style theorems for distinction equations are provided within the framework of the Lagrangian and Hamiltonian formalism for distinction equations.
In addition, the booklet develops distinction mesh geometry according to a symmetry staff, simply because diverse symmetries are proven to require diverse geometric mesh constructions. the tactic of finite-difference invariants presents the mesh producing equation, any targeted case of which promises the mesh invariance. a few examples of invariant meshes is gifted. particularly, and with a number 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 booklet 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 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