By Vladimir Dorodnitsyn

Intended for researchers, numerical analysts, and graduate scholars in a number 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 building 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 makes a speciality of the upkeep of entire 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 traditional distinction equations.

A mammoth a part of the e-book is anxious with conservation legislation and primary integrals for distinction versions. The variational procedure and Noether kind 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 response to a symmetry team, simply because assorted symmetries are proven to require various geometric mesh buildings. the strategy of finite-difference invariants offers the mesh producing equation, any distinctive case of which promises the mesh invariance. a couple of examples of invariant meshes is gifted. specifically, and with various functions in numerics for non-stop media, that the majority evolution PDEs must be approximated on relocating meshes.

Based at the constructed approach to finite-difference invariants, the sensible sections of the ebook 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.

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

Ordinary Differential Equations: 0 (Undergraduate Texts in Mathematics)

In contrast to such a lot texts in differential equations, this textbook supplies an early presentation of the Laplace remodel, that is then used to inspire and increase the various closing differential equation suggestions for which it really is fairly like minded. for instance, the traditional resolution equipment for consistent coefficient linear differential equations are fast and simplified, and answer equipment for consistent coefficient structures are streamlined.

Concepts and Results in Chaotic Dynamics: A Short Course (Theoretical and Mathematical Physics)

The learn of dynamical platforms is a good demonstrated box. This booklet offers a landscape of numerous elements of curiosity to mathematicians and physicists. It collects the cloth of numerous classes on the graduate point given through the authors, averting precise proofs in trade for varied illustrations and examples.

An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs (Publications of the Scuola Normale Superiore)

This quantity offers with the regularity conception for elliptic structures. We may perhaps locate the foundation of this type of concept in of the issues posed via David Hilbert in his celebrated lecture brought in the course of the foreign Congress of Mathematicians in 1900 in Paris:19th challenge: Are the suggestions to average difficulties within the Calculus of adaptations continuously unavoidably analytic?

Isolated Singularities in Partial Differential Inequalities (Encyclopedia of Mathematics and its Applications)

During this monograph, the authors current a few robust tools for facing singularities in elliptic and parabolic partial differential inequalities. the following, the authors take the original procedure of investigating differential inequalities instead of equations, the reason is that the easiest method to learn an equation is frequently to review a corresponding inequality; for instance, utilizing sub and superharmonic capabilities to review harmonic capabilities.

Additional resources for Applications of Lie Groups to Difference Equations (Differential and Integral Equations and Their Applications)

Example text

Download PDF sample

Rated 4.86 of 5 – based on 42 votes