Related papers: Notes on Lie symmetry group methods for differenti…
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…
In the present paper the classical point symmetry analysis is extended from partial differential to functional differential equations with functional derivatives. In order to perform the group analysis and deal with the functional…
Lie group method provides an efficient tool to solve a differential equation. This paper suggests a fractional partner for fractional partial differential equations using a fractional characteristic method. A space-time fractional diffusion…
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…
We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry preserving discretization provides difference schemes for which…
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.
In this note we survey results in recent research papers on the use of Lie groups in the study of partial differential equations. The focus will be on parabolic equations, and we will show how the problems at hand have solutions that seem…
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…
Methods of Lie group analysis of differential equations are extended to weak solutions of (linear and nonlinear) PDEs, where the term ``weak solution'' comprises the following settings: (a) Distributional solutions. (b) Solutions in…
The theory of Lie remarkable equations, i.e. differential equations characterized by their Lie point symmetries, is reviewed and applied to ordinary differential equations. In particular, we consider some relevant Lie algebras of vector…
A powerful method for solving non-linear first-order ordinary differential equations, which is based on geometrical understanding of the corresponding dynamics of the so called Lie systems, is developed. This method allows us not only to…
Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an…
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…
We present an extension of the methods of classical Lie group analysis of differential equations to equations involving generalized functions (in particular: distributions). A suitable framework for such a generalization is provided by…
This article reviews the use of differential forms and Lie derivatives to find symmetries of differential equations, as originally presented by Harrison and Estabrook, J. Math. Phys., 12 (1971), 653. An outline of the method is given,…
We give a short and elementary introduction to Lie group methods. A selection of applications of Lie group integrators are discussed. Finally, a family of symplectic integrators on cotangent bundles of Lie groups is presented and the notion…
A set of linear second-order differential equations is converted into a semigroup, whose algebraic structure is used to generate many novel equations. Two independent methods that can be used to derive the equations of the semigroup are…
These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
We present a generalization of Lie's method for finding the group invariant solutions to a system of partial differential equations. Our generalization relaxes the standard transversality assumption and encompasses the common situation…