The main purpose of this article is to show how symmetry structures in partial differential equations can be preserved in a discrete world and reflected in difference schemes. Three different structure preserving discretizations of the Liouville equation are presented and then used to solve specific boundary value problems. The results are compared with exact solutions satisfying the same boundary conditions. All three discretizations are on four point lattices. One preserves linearizability of the equation, another the infinite-dimensional symmetry group as higher symmetries, the third one preserves the maximal finite-dimensional subgroup of the symmetry group as point symmetries. A 9-point invariant scheme that gives a better approximatio...
We show how to compute the discrete symmetries for a given Black-Scholes (B-S) partial differential ...
AbstractAre positive solutions of finite difference boundary value problems Δhu=f(u) in Ωh, u=0 on ∂...
Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and p...
The main purpose of this article is to show how symmetry structures in par- tial differential equati...
The symmetry algebra of the real elliptic Liouville equation is an infinite-dimensional loop algebra...
The Liouville equation is well known to be linearizable by a point transformation. It has an infinit...
We briefly review two different methods of applying Lie group theory in the numerical solution of or...
We look at numerical methods for differential equations which are invariant under the action of a sy...
In this article we show that we can carry out the symmetry preserving discretization of the Boussine...
This paper describes a method that enables the user to construct systematically the set of all discr...
Different symmetry formalisms for difference equations on lattices are reviewed and applied to perfo...
Given a differential equation that admits a group of symmetries, it is frequently desirable to prese...
Lie symmetries has been introduced by Sophus Lie to study differential equations. It has been one of...
A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in ful...
In this note we present some ideas on when Lie symmetries, both point and generalized, can depend on...
We show how to compute the discrete symmetries for a given Black-Scholes (B-S) partial differential ...
AbstractAre positive solutions of finite difference boundary value problems Δhu=f(u) in Ωh, u=0 on ∂...
Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and p...
The main purpose of this article is to show how symmetry structures in par- tial differential equati...
The symmetry algebra of the real elliptic Liouville equation is an infinite-dimensional loop algebra...
The Liouville equation is well known to be linearizable by a point transformation. It has an infinit...
We briefly review two different methods of applying Lie group theory in the numerical solution of or...
We look at numerical methods for differential equations which are invariant under the action of a sy...
In this article we show that we can carry out the symmetry preserving discretization of the Boussine...
This paper describes a method that enables the user to construct systematically the set of all discr...
Different symmetry formalisms for difference equations on lattices are reviewed and applied to perfo...
Given a differential equation that admits a group of symmetries, it is frequently desirable to prese...
Lie symmetries has been introduced by Sophus Lie to study differential equations. It has been one of...
A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in ful...
In this note we present some ideas on when Lie symmetries, both point and generalized, can depend on...
We show how to compute the discrete symmetries for a given Black-Scholes (B-S) partial differential ...
AbstractAre positive solutions of finite difference boundary value problems Δhu=f(u) in Ωh, u=0 on ∂...
Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and p...
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