相关论文: Lie point symmetries of difference equations and l…
A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and on the lattice. They take solutions into solutions and can be…
We show that any first order ordinary differential equation with a known Lie point symmetry group can be discretized into a difference scheme with the same symmetry group. In general, the lattices are not regular ones, but must be adapted…
Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study…
Symmetry is a powerful tool for finding analytical solutions to differential equations, both partial and ordinary, via the similarity variables or via the invariance of the equation under group transformations. It is the largest group of…
A full Lie point symmetry analysis of rational difference equations is performed. Non-trivial symmetries are derived and exact solutions using these symmetries are obtained.
Fundamentals on Lie group methods and applications to differential equations are surveyed. Many examples are included to elucidate their extensive applicability for analytically solving both ordinary and partial differential equations.
We present an algorithm for determining the Lie point symmetries of differential equations on fixed non transforming lattices, i.e. equations involving both continuous and discrete independent variables. The symmetries of a specific…
Different symmetry formalisms for difference equations on lattices are reviewed and applied to perform symmetry reduction for both linear and nonlinear partial difference equations. Both Lie point symmetries and generalized symmetries are…
A Mathematica based program has been elaborated in order to determine the symmetry group of a finite difference equation, by means of its differential representation. The package provides functions which enable us to solve the determining…
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 examples of the construction of invariant…
Lie symmetry group method is applied to study the Telegraph equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra…
Lie symmetry analysis is one of the powerful tools to analyze nonlinear ordinary differential equations. We review the effectiveness of this method in terms of various symmetries. We present the method of deriving Lie point symmetries,…
In this paper, we show that when two systems of differential equations admitting a symmetry group are related by a point transformation it is always possible to generate invariant schemes, one for each system, that are also related by the…
Classical Lie group theory provides a universal tool for calculating symmetry groups for systems of differential equations. However Lie's method is not as much effective in the case of integral or integro-differential equations as well as…
When we consider a differential equation $\Delta=0$ whose set of solutions is ${{\cal S}}_\Delta$, a Lie-point exact symmetry of this is a Lie-point invertible transformation $T$ such that $T({{\cal S}}_\Delta)={{\cal S}}_\Delta$, i.e. such…
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 ways of addressing this difficulty is to…
Lie-symmetry methods are used to determine the symmetry group of reduced magnetohydrodynamics. This group allows for arbitrary, continuous transformations of the fields themselves, along with space-time transformations. The derivation…
Symmetry preserving difference schemes approximating second and third order ordinary differential equations are presented. They have the same three or four-dimensional symmetry groups as the original differential equations. The new…
We extend two of the methods previously introduced to find discrete symmetries of differential equations to the case of difference and differential-difference equations. As an example of the application of the methods, we construct the…
Lie symmetry group method is applied to study the boundary-layer equations for two-dimensional steady flow of an incompressible, viscous fluid near a stagnation point at a heated stretching sheet placed in a porous medium equation. The…