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 e-book to supply a scientific development of invariant distinction schemes for nonlinear differential equations. A advisor to equipment and ends up in a brand new region of software of Lie teams to distinction equations, distinction meshes (lattices), and distinction functionals, this publication specializes in the renovation 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 monstrous a part of the booklet is anxious with conservation legislation and primary integrals for distinction types. The variational procedure and Noether variety theorems for distinction equations are provided within the framework of the Lagrangian and Hamiltonian formalism for distinction equations.
In addition, the ebook develops distinction mesh geometry in line with a symmetry staff, simply because diversified symmetries are proven to require varied geometric mesh constructions. the strategy of finite-difference invariants offers the mesh producing equation, any detailed 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 almost all evolution PDEs must be approximated on relocating meshes.
Based at the constructed 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 recognized 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