A Comparison Between Laguerre, Hermite, and Sinc Orthogonal Functions

TL;DR

This paper compares the effectiveness of Laguerre, Hermite, and Sinc orthogonal functions in spectral methods for solving differential equations over an infinite interval, demonstrating their relative performance on selected problems.

Contribution

It introduces a comparative analysis of Laguerre, Hermite, and Sinc functions in spectral collocation methods for differential equations on unbounded domains.

Findings

Laguerre functions perform well on certain problems

Hermite functions are effective for others

Sinc functions offer a different trade-off in accuracy

Abstract

A series of problems in different fields such as physics and chemistry are modeled by differential equations. Differential equations are divided into partial differential equations and ordinary differential equations which can be linear or nonlinear. One approach to solve those kinds of equations is using orthogonal functions into spectral methods. In this paper, we firstly describe Laguerre, Hermite, and Sinc orthogonal functions. Secondly, we select three interesting problems which are modeled as differential equations over the interval $[0, +\infty)$. Then, we use the collocation method as a spectral method for solving those selected problems and compare the performance of Laguerre, Hermite, and Sinc orthogonal functions in solving those types of equations.