Symmetry-preserving discrete schemes for some heat transfer equations

TL;DR

This paper presents three characteristic examples of the construction of invariant difference equations and meshes, where the original continuous symmetries are preserved in discrete models.

Abstract

Lie group analysis of differential equations is a generally recognized method, which provides invariant solutions, integrability, conservation laws etc. In this paper we present three characteristic examples of the construction of invariant difference equations and meshes, where the original continuous symmetries are preserved in discrete models. Conservation of symmetries in difference modeling helps to retain qualitative properties of the differential equations in their difference counterparts.

Figures (8)

• Figure 1: The stencil of the orthogonal mesh.
• Figure 2: An evolutionary mesh with flat time-layers.
• Figure 3: The stencil of the evolutionary mesh.
• Figure 4: Deformation of the orthogonal mesh.
• Figure 5: Solution of the invariant model.