A Comparison Between Laguerre, Hermite, and Sinc Orthogonal Functions
An incremental comparison of known orthogonal functions for solving differential equations, lacking concrete performance data.
This paper compares Laguerre, Hermite, and Sinc orthogonal functions for solving differential equations on semi-infinite intervals using the collocation method, but provides no quantitative results or performance metrics.
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.