2009 journal article

Fourier series of half-range functions by smooth extension

APPLIED MATHEMATICAL MODELLING, 33(2), 812–821.

co-author countries: United States of America πŸ‡ΊπŸ‡Έ
author keywords: Fourier series; Smooth extension; Half-range problems
Source: Web Of Science
Added: August 6, 2018

This paper considers Fourier series approximations of one- and two-dimensional functions over the half-range, that is, over the sub-interval [0, L ] of the interval [βˆ’ L, L ] in one-dimensional problems and over the sub-domain [0, L x ] Γ— [0, L y ] of the domain [βˆ’ L x , L x ] Γ— [βˆ’ L y , L y ] in two-dimensional problems. It is shown how to represent these functions using a Fourier series that employs a smooth extension. The purpose of the smooth extension is to improve the convergence characteristics otherwise obtained using the even and odd extensions. Significantly improved convergence characteristics are illustrated in one-dimensional and two-dimensional problems.