LIE ALGEBRAIC DISCRETIZATION OF DIFFERENTIAL EQUATIONS

Lie - algebraic discretization of differential equations by Yuri Smirnov

A certain representation for the Heisenberg algebra in finitedifference operators is established. The Lie-algebraic procedure of discretization of differential equations with isospectral property is proposed. Using sl2-algebra based approach, (quasi)-exactlysolvable finite-difference equations are described. It is shown that the operators having the Hahn, Charlier and Meixner polynomials as the...

Solution of linear partial differential equations by Lie algebraic methods

A new algorithm is proposed for obtaining explicit solutions of the Cauchy problem defined by a certain class of partial differential equations (PDE) of parabolic type. The algorithm exploits the algebraic structure of the problem to transform the PDE into an ordinary matrix differential equation, which is then solved by Lie algebraic techniques.

Galois Theory of Differential Equations, Algebraic Groups and Lie Algebras

As a consequence the level of exposition varies considerably. In particular, some proofs (marked by ¶) and the Appendix require more mathematical background than the main body of the text. The reader is advised to study the paper without paying too much attention to those technical details. This gives sufficient information to complete the exercises. We hope that this introduction might motivat...

Solving Partial Differential Equations by Lie Algebraic Methods

Reduction of Differential Equations by Lie Algebra of Symmetries

The paper is devoted to an application of Lie group theory to differential equations. The basic infinitesimal method for calculating symmetry group is presented, and used to determine general symmetry group of some differential equations. We include a number of important applications including integration of ordinary differential equations and finding some solutions of partial differential equa...