Abstract

A difference scheme for the transfer problem, constructed as a linear combination of the Cabaret scheme and the central difference scheme, is proposed. The stability and dispersion properties of the scheme are studied. It is shown that the constructed scheme has the best dispersion properties for high-frequency harmonics at small Courant numbers compared with the known Cabaret scheme for the transport equation. A comparison is made of the errors of this scheme and the two-parameter third-order difference accuracy scheme based on the numerical experiments on the previously used test problem sets. It is shown that in the normal grid space L₁ the developed scheme has smaller errors and also uses a more compact template (in calculating the inode the node values i – 1, i, and i + 1 are used), and the transition to the next time layer is carried out for a smaller number of arithmetic operations.

中文翻译：

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具有改进的色散特性的歌舞表演差异方案

摘要

提出了一种针对转移问题的差分方案，该方案由Cabaret方案和中央差分方案的线性组合构成。研究了该方案的稳定性和分散性。结果表明，与运输方程式的已知Cabaret方案相比，所构造的方案在小Courant数下具有最佳的高频谐波色散特性。基于先前使用的测试问题集的数值实验，对该方案和两参数三阶差分精度方案的误差进行了比较。结果表明，在正常电网空间大号_1个的发达方案具有较小的误差，并且也使用了更紧凑的模板（在计算我节点的节点值我– 1，i和i + 1），并以较少的算术运算数执行到下一个时间层的转换。