Generating the Laguerre expansion coefficients by solving a one-dimensional transport equation

Abstract

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.