Convolution integrals and formulas for the Christov functions

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    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.

    Original languageEnglish
    Title of host publicationApplication of Mathematics in Technical and Natural Sciences - 13th International Hybrid Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2021
    EditorsMichail D. Todorov
    PublisherAmerican Institute of Physics Inc.
    ISBN (Electronic)9780735443617
    DOIs
    Publication statusPublished - 26 Sept 2022
    Event13th International Hybrid Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2021 - Albena, Bulgaria
    Duration: 24 Jun 202129 Jun 2021

    Publication series

    NameAIP Conference Proceedings
    Volume2522
    ISSN (Print)0094-243X
    ISSN (Electronic)1551-7616

    Conference

    Conference13th International Hybrid Conference for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2021
    Country/TerritoryBulgaria
    CityAlbena
    Period24/06/2129/06/21

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