Four Points Linearizable Lattice Schemes

TL;DR

This paper establishes conditions under which four-point lattice schemes can be linearized through point transformations and applies these conditions to a specific difference scheme, demonstrating its non-linearizability.

Contribution

It introduces criteria for linearizability of four-point lattice schemes and applies them to a symmetry-preserving difference scheme for the potential Burgers equation.

Findings

The conditions for linearizability are explicitly derived.

The symmetry-preserving difference scheme for potential Burgers is shown not to be linearizable.

Provides a method to test linearizability of lattice schemes.

Abstract

We provide conditions for a lattice scheme defined on a four points lattice to be linearizable by a point transformation. We apply the obtained conditions to a symmetry preserving difference scheme for the potential Burgers introduced by Dorodnitsyn \cite{db} and show that it is not linearizable.