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Symmetries of systems of stochastic differential equations with diffusion matrices of full rank

- R. Kozlov
- Mathematics
- 18 June 2010

Lie point symmetries of a system of stochastic differential equations (SDEs) with diffusion matrices of full rank are considered. It is proved that the maximal dimension of a symmetry group admitted… Expand

Invariance and first integrals of continuous and discrete Hamiltonian equations

- V. Dorodnitsyn, R. Kozlov
- Mathematics, Physics
- 10 June 2009

The relation between symmetries and first integrals for both continuous canonical Hamiltonian equations and discrete Hamiltonian equations is considered. The observation that canonical Hamiltonian… Expand

Continuous symmetries of Lagrangians and exact solutions of discrete equations

- V. Dorodnitsyn, R. Kozlov, P. Winternitz
- Physics, Mathematics
- 23 July 2003

One of the difficulties encountered when studying physical theories in discrete space–time is that of describing the underlying continuous symmetries (like Lorentz, or Galilei invariance). One of the… Expand

Symmetry-preserving difference schemes for some heat transfer equations

- M. Bakirova, V. Dorodnitsyn, R. Kozlov
- Mathematics, Physics
- 7 December 1997

Lie group analysis of differential equations is a generally recognized method, which provides invariant solutions, integrability, conservation laws etc. In this paper we present three characteristic… Expand

A Heat Transfer with a Source: the Complete Set of Invariant Difference Schemes

- V. Dorodnitsyn, R. Kozlov
- Mathematics
- 1 January 2003

Abstract In this letter we present the set of invariant difference equations and meshes which preserve the Lie group symmetries of the equation u t=(K(u)u x)x + Q(u). All special cases of K(u) and… Expand

The behaviour of the local error in splitting methods applied to stiff problems

Splitting methods are frequently used in solving stiff differential equations and it is common to split the system of equations into a stiff and a nonstiff part. The classical theory for the local… Expand

On maximal Lie point symmetry groups admitted by scalar stochastic differential equations

- R. Kozlov
- Mathematics
- 20 May 2011

It is proved that the Lie point symmetry group admitted by a scalar stochastic differential equation (SDE) of order n ≥ 3 is at most (n + 2) dimensional. This result supplements those for first- and… Expand

The group classification of a scalar stochastic differential equation

- R. Kozlov
- Mathematics
- 12 January 2010

Lie point group classification of a scalar stochastic differential equation (SDE) with one-dimensional Brownian motion is presented. The admitted symmetry group can be zero, one, two or three… Expand

On symmetries of stochastic differential equations

- R. Kozlov
- Mathematics
- 1 December 2012

Abstract This note can be considered as a supplement to article [8] . Its purpose is twofold. First, to show that symmetries of Ito stochastic differential equations form a Lie algebra. Second, to… Expand

First integrals of difference Hamiltonian equations

- V. Dorodnitsyn, R. Kozlov
- Mathematics
- 27 October 2009

In the present paper, the well-known Noether's identity, which represents the connection between symmetries and first integrals of Euler-Lagrange equations, is rewritten in terms of the Hamiltonian… Expand

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