Abstract The univariate direct quadrature spanning tree (DQST) method was evaluated with respect to accuracy and computational cost. This included a convergence analysis over the discretization of the breakage term and an accuracy analysis of the smoothing procedure. We also proposed many enhancements to the method, including a second-order time integration scheme, a new initialization method and its extension for cases involving growth. We have shown that the original smoothing procedure does not conserve the second-order moment of the distribution. In order to guarantee its conservation, a new smoothing method was proposed. The usage of the new smoothing method combined with the second-order time integration scheme reduced the moment errors by several orders of magnitude with a modest increase in the computational cost.

中文翻译：

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单变量直接正交生成树法的扩展与收敛分析

摘要 对单变量直接正交生成树 (DQST) 方法的准确性和计算成本进行了评估。这包括对破损项离散化的收敛分析和平滑程序的准确性分析。我们还提出了对该方法的许多改进，包括二阶时间积分方案、新的初始化方法及其对涉及增长的情况的扩展。我们已经证明，原始平滑程序不守恒分布的二阶矩。为了保证其守恒性，提出了一种新的平滑方法。使用新的平滑方法与二阶时间积分方案相结合，将矩误差降低了几个数量级，同时适度增加了计算成本。