A Comparison Between Laguerre, Hermite, and Sinc Orthogonal Functions

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.

💡 Research Summary

The paper investigates the use of three orthogonal function families—modified generalized Laguerre, transformed Hermite, and transformed Sinc functions—as basis functions in a collocation spectral method for solving differential equations defined on the semi‑infinite interval (