March 21, 2018

New PDF release: Applications of Lie Groups to Difference Equations

By Vladimir Dorodnitsyn

ISBN-10: 1138118230

ISBN-13: 9781138118232

ISBN-10: 1420083090

ISBN-13: 9781420083095

Intended for researchers, numerical analysts, and graduate scholars in numerous fields of utilized arithmetic, physics, mechanics, and engineering sciences, Applications of Lie teams to distinction Equations is the 1st booklet to supply a scientific development of invariant distinction schemes for nonlinear differential equations. A advisor to equipment and leads to a brand new quarter of software of Lie teams to distinction equations, distinction meshes (lattices), and distinction functionals, this publication specializes in the maintenance of whole symmetry of unique differential equations in numerical schemes. This symmetry protection leads to symmetry aid of the adaptation version besides that of the unique partial differential equations and so as aid for usual distinction equations.

A giant a part of the booklet is anxious with conservation legislation and primary integrals for distinction types. The variational technique 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 in line with a symmetry crew, simply because diversified symmetries are proven to require various geometric mesh constructions. the tactic of finite-difference invariants offers the mesh producing equation, any distinct case of which promises the mesh invariance. a few examples of invariant meshes is gifted. particularly, and with various 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 e-book 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.

Show description

Read Online or Download Applications of Lie Groups to Difference Equations (Differential and Integral Equations and Their Applications) PDF

Best differential equations books

Download e-book for iPad: Matched Asymptotic Expansions in Reaction-Diffusion Theory by J.A. Leach,D.J. Needham

This quantity features a wealth of effects and methodologies appropriate to quite a lot of difficulties bobbing up in reaction-diffusion thought. it may be seen either as a guide, and as an in depth description of the technique. The authors current new equipment according to matched asymptotic expansions.

Get Methods of Small Parameter in Mathematical Biology (Modeling PDF

This monograph provides new instruments for modeling multiscale organic tactics. usual techniques are typically pushed by way of mechanisms extensively differing from one another within the time or house scale at which they function and therefore could be defined by means of applicable multiscale versions. besides the fact that, taking a look at all such scales at the same time is frequently infeasible, expensive, and gives info that's redundant for a selected program.

Download PDF by Nail H. Ibragimov,Jörg Volkmann: Differentialgleichungen und Mathematische Modellbildung:

Dieses Lehrbuch führt in das Gebiet der Differentialgleichungen und der mathematischen Modellbildung ein. Dabei werden etablierte und moderne Rechenmethoden besprochen und es wird erläutert, wie diese zur mathematischen Modellierung benutzt werden können. Lie-Gruppen und deren Einsatz zur Lösung von Differentialgleichungen spielen dabei eine tragende Rolle.

Extra info for Applications of Lie Groups to Difference Equations (Differential and Integral Equations and Their Applications)

Example text

Download PDF sample

Applications of Lie Groups to Difference Equations (Differential and Integral Equations and Their Applications) by Vladimir Dorodnitsyn

by Kenneth

Rated 4.34 of 5 – based on 27 votes