In this paper we focus on the L-stable ${\beta }_1/{\beta }_2$-Bathe time integration method to obtain new insights for transient and wave propagation solutions. The method is a specific case of the ${\rho }_{\infty }$- Bathe scheme but deserves special attention because it can be used directly as a first-order and second-order scheme effective in certain analyses. We show how the parameters ${\beta }_1$ and ${\beta }_2$ can be used to introduce appropriate numerical damping and illustrate the theoretical findings through the solution of some wave propagation problems.

中文翻译：

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新的见解β ₁ / β ₂ -Bathe时间积分方案时大号稳定版

在本文中，我们重点介绍L稳定 ${\beta }_{\mathrm{1个}}/{\beta }_2$-沐浴时间积分方法，以获得有关瞬态和波传播解决方案的新见解。该方法是特定情况下的${\rho }_{\infty }$-洗澡方案，但值得特别注意，因为它可以直接用作有效的某些分析中的一阶和二阶方案。我们展示了参数${\beta }_{\mathrm{1个}}$ 和 ${\beta }_2$ 可以用来引入适当的数值阻尼，并通过解决一些波传播问题来说明理论发现。