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Symmetries of systems of stochastic differential equations with diffusion matrices of full rank
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 admittedExpand
Invariance and first integrals of continuous and discrete Hamiltonian equations
The relation between symmetries and first integrals for both continuous canonical Hamiltonian equations and discrete Hamiltonian equations is considered. The observation that canonical HamiltonianExpand
Continuous symmetries of Lagrangians and exact solutions of discrete equations
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 theExpand
Symmetry-preserving difference schemes for some heat transfer equations
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 characteristicExpand
A Heat Transfer with a Source: the Complete Set of Invariant Difference Schemes
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) andExpand
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 localExpand
On maximal Lie point symmetry groups admitted by scalar stochastic differential equations
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- andExpand
The group classification of a scalar stochastic differential equation
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 threeExpand
On symmetries of stochastic differential equations
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, toExpand
First integrals of difference Hamiltonian equations
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 HamiltonianExpand
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