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

TL;DR

This paper introduces a novel method for calculating Laguerre expansion coefficients by solving a one-dimensional transport equation, offering improved stability, accuracy, and efficiency over traditional integral computation methods.

Contribution

It proposes a new algorithm that computes Laguerre transform coefficients via a transport equation, enhancing stability and accuracy compared to direct integral calculations.

Findings

Better stability in coefficient calculation

Higher accuracy in Laguerre series expansion

Reduced computational burden

Abstract

Spectral methods based on integral transforms may be efficiently used to solve differential equations in some special cases. This paper considers a different 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.