@inproceedings{510bfac7c01b4eae9bf497bc2d6d64c0,
title = "Convolution integrals and formulas for the Christov functions",
abstract = "The Christov real-valued functions were introduced as the combination of the Wiener functions. The functions were and are used as a basis system when a spectral method is applied to soliton problems in L2(-∞, +∞). The functions have proven to be a very useful and reliable numerical tool for the investigation of such problems. The number of terms required in a Christov-Galerkin expansion to obtain very good results is quite small in comparison with other basis systems. The efficiency and accuracy of the method can be further improved if the expansion is centered at a point other than the origin. The necessary convolution integrals of the form ∫-∞∞Cn(x)Ck(x-y)dx, ∫-∞∞Sn(x)Sk(x-y)dx, ∫-∞∞Sn(x)Ck(x-y)dx are computed, enabling the expansion of the shifted Christov functions into Christov functions and vice-versa. The accuracy of the expansions is tested numerically.",
author = "Christou, {M. A.} and Papanicolaou, {N. C.}",
note = "Publisher Copyright: {\textcopyright} 2022 Author(s).; 13th International Hybrid Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2021 ; Conference date: 24-06-2021 Through 29-06-2021",
year = "2022",
month = sep,
day = "26",
doi = "10.1063/5.0101443",
language = "English",
series = "AIP Conference Proceedings",
publisher = "American Institute of Physics Inc.",
editor = "Todorov, {Michail D.}",
booktitle = "Application of Mathematics in Technical and Natural Sciences - 13th International Hybrid Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2021",
}