Publisher:

Chapman & Hall/CRC

Number of Pages:

264

Price:

89.95

ISBN:

9781420083095

Date Received:

Tuesday, December 14, 2010

Reviewable:

No

Reviewer Email Address:

Series:

Differential and Integral Equations and Their Applications

Publication Date:

2011

Format:

Hardcover

Audience:

Category:

Monograph

**Preface Introduction **Brief introduction to Lie group analysis of differential equations

Preliminaries: Heuristic approach in examples

Difference analog of the Leibniz rule

Invariant difference meshes

Transformations preserving the geometric meaning of finite-difference derivatives

Newton’s group and Lagrange’s formula

Commutation properties and factorization of group operators on uniform difference meshes

Finite-difference integration and prolongation of the mesh space to nonlocal variables

Change of variables in the mesh space

Symmetry preservation in difference modeling: Method of finite-difference invariants

Examples of construction of difference models preserving the symmetry of the original continuous models

Invariant second-order difference equations and lattices

Symmetry preserving difference schemes for the linear heat equation

Invariant difference models for the Burgers equation

Invariant difference model of the heat equation with heat flux relaxation

Invariant difference model of the Korteweg–de Vries equation

Invariant difference model of the nonlinear Shrödinger equation

Partial delay differential equations

Symmetry of differential-difference equations

Lagrangian Formalism for Difference Equations

Discrete representation of Euler’s operator

Criterion for the invariance of difference functionals

Invariance of difference Euler equations

Variation of difference functional and quasi-extremal equations

Invariance of global extremal equations and properties of quasiextremal equations

Conservation laws for difference equations

Noether-type identities and difference analog of Noether’s theorem

Necessary and sufficient conditions for global extremal equations to be invariant

Applications of Lagrangian formalism to second-order difference equations

Moving mesh schemes for the nonlinear Shrödinger equation

Variational statement of the difference Hamiltonian equations

Symplecticity of difference Hamiltonian equations

Invariance of the Hamiltonian action

Difference Hamiltonian identity and Noether-type theorem for difference Hamiltonian equations

Invariance of difference Hamiltonian equations

Examples

Three-point exact schemes for nonlinear ODE

Index

Publish Book:

Modify Date:

Tuesday, December 14, 2010

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