A new approach for calculating Laguerre expansion coefficients is proposed. In solving applied problems, initial data may be specified as time series with a constant discretization step. In this case, the use of quadratures of high-order accuracy is limited due to their instability. In order to overcome these difficulties, this paper considers an approach in which algorithms are proposed to calculate integral Laguerre transform by solving a one-dimensional transport equation. In contrast to the direct calculation of improper integrals of rapidly oscillating functions, these procedures make it possible to calculate the expansion coefficients of a Laguerre series expansion with better stability, higher accuracy, and less computational burden. The numerical experiments have shown that the methods are economical in terms of operation count, stable, and have reasonable accuracy in practical calculations.

提出了一种计算拉盖尔膨胀系数的新方法。在解决应用问题时，可以将初始数据指定为具有恒定离散步骤的时间序列。在这种情况下，由于其不稳定性，限制了高阶精度正交的使用。为了克服这些困难，本文考虑了一种方法，该方法提出了一种通过求解一维输运方程来计算积分Laguerre变换的算法。与直接计算快速振荡函数的不适当积分相比，这些过程使得可以计算Laguerre级数展开式的展开系数，具有更好的稳定性，更高的准确性和更少的计算负担。数值实验表明，该方法在操作次数，稳定性，稳定性方面都是经济的。