First integrals of ordinary difference equations beyond Lagrangian methods

Abstract

A new method for finding first integrals of discrete equations is presented. It can be used for discrete equations which do not possess a variational (Lagrangian or Hamiltonian) formulation. The method is based on a newly established identity which links symmetries of the underlying discrete equations, solutions of the discrete adjoint equations and first integrals. The method is applied to invariant mappings and discretizations of a second order and a third order ODEs. In examples the set of independent first integrals makes it possible to find the general solution of the discrete equations. The method is compared to a direct method of constructing first integrals.

References in corpus (1)

• Difference schemes with point symmetries and their numerical tests

Cited by in corpus (4)

• Structure Preserving Discretizations of the Liouville Equation and their Numerical Tests
• The Korteweg-de Vries equation and its symmetry-preserving discretization
• Self-adjointness and conservation laws of difference equations
• Computation of Infinitesimals for a Group Action on a Multispace of One Independent Variable