منابع مشابه
Lie Symmetries of Difference Equations
The discrete heat equation is worked out in order to illustrate the search of symmetries of difference equations. It is paid an special attention to the Lie structure of these symmetries, as well as to their dependence on the derivative discretization. The case of q–symmetries for discrete equations in a q–lattice is also considered.
متن کاملLie Symmetries of Multidimensional Difference Equations
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 used to perform symmetry reduction. The method generalizes one presented in a recent publication for the case of ordinary difference equations. In turn, it ...
متن کاملLie point symmetries of difference equations and lattices
A method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the corresponding difference scheme invariant. The method is applied to several examples. The found symmetry groups are used to obtain particular solutions of differential-difference equations.
متن کاملGeneralized Cauchy Difference Equations. Ii
The main result is an improvement of previous results on the equation f(x) + f(y)− f(x+ y) = g[φ(x) + φ(y)− φ(x+ y)] for a given function φ. We find its general solution assuming only continuous differentiability and local nonlinearity of φ. We also provide new results about the more general equation f(x) + f(y)− f(x+ y) = g(H(x, y)) for a given function H. Previous uniqueness results required ...
متن کاملApproximate Lie Group Analysis of Finite–difference Equations
Approximate group analysis technique, that is, the technique combining the methodology of group analysis and theory of small perturbations, is applied to finite–difference equations approximating ordinary differential equations. Finite–difference equations are viewed as a system of algebraic equations with a small parameter, introduced through the definitions of finite–difference derivatives. I...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1972
ISSN: 0022-247X
DOI: 10.1016/0022-247x(72)90211-9