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 e-book to supply a scientific development of invariant distinction schemes for nonlinear differential equations. A consultant to tools and leads to a brand new quarter of software of Lie teams to distinction equations, distinction meshes (lattices), and distinction functionals, this booklet makes a speciality of the maintenance of entire symmetry of unique differential equations in numerical schemes. This symmetry upkeep ends up in symmetry aid of the adaptation version in addition to that of the unique partial differential equations and so as relief for traditional distinction equations.
A large a part of the e-book is anxious with conservation legislation and primary integrals for distinction types. The variational method and Noether style theorems for distinction equations are awarded within the framework of the Lagrangian and Hamiltonian formalism for distinction equations.
In addition, the e-book develops distinction mesh geometry according to a symmetry team, simply because diverse symmetries are proven to require assorted geometric mesh buildings. the strategy of finite-difference invariants offers the mesh producing equation, any designated case of which promises the mesh invariance. a few examples of invariant meshes is gifted. particularly, and with various functions 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 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 Schrödinger equation.
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