Symmetry-preserving discrete schemes for some heat transfer equations
Margarita Bakirova, Vladimir Dorodnitsyn and Roman Kozlov
微分方程的 Lie group 分析是一种公认的方法,它提供不变的解、可集成性、保护定律等。 在本文中,我们介绍了构造不变差方程和网格的三个特征示例,其中原始连续对称保存在离散模型中。 在差分建模中保护对称性有助于在其差异对应物中保留微分方程的定性性质。
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...