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Summation Method for Fourier Series Associated with a Mixed Problem for the Inhomogeneous Telegraph Equation.

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Title: Summation Method for Fourier Series Associated with a Mixed Problem for the Inhomogeneous Telegraph Equation.
Authors: Lomov, I. S.1 (AUTHOR) lomov@cs.msu.ru
Source: Computational Mathematics & Mathematical Physics. Mar2025, Vol. 65 Issue 3, p522-528. 7p.
Subjects: Fourier series, Separation of variables, Statistical smoothing, Telegraph & telegraphy, Equations
Abstract: A summation method for Fourier series associated with a generalized mixed problem for the telegraph equation in a semi-infinite strip is proposed. The concept of the regularity of a summation method is introduced. It is shown that the generalized sum produced by this method can be used as a solution of the generalized mixed problem. Here, the generalized sum is specified by an exponentially converging function series. In the case of smooth initial data, this series gives a strong solution of the original pro-blem. [ABSTRACT FROM AUTHOR]
Copyright of Computational Mathematics & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Summation Method for Fourier Series Associated with a Mixed Problem for the Inhomogeneous Telegraph Equation.
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  Data: <searchLink fieldCode="JN" term="%22Computational+Mathematics+%26+Mathematical+Physics%22">Computational Mathematics & Mathematical Physics</searchLink>. Mar2025, Vol. 65 Issue 3, p522-528. 7p.
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  Label: Abstract
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  Data: A summation method for Fourier series associated with a generalized mixed problem for the telegraph equation in a semi-infinite strip is proposed. The concept of the regularity of a summation method is introduced. It is shown that the generalized sum produced by this method can be used as a solution of the generalized mixed problem. Here, the generalized sum is specified by an exponentially converging function series. In the case of smooth initial data, this series gives a strong solution of the original pro-blem. [ABSTRACT FROM AUTHOR]
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  Label:
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  Data: <i>Copyright of Computational Mathematics & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1134/S0965542524702117
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 7
        StartPage: 522
    Subjects:
      – SubjectFull: Fourier series
        Type: general
      – SubjectFull: Separation of variables
        Type: general
      – SubjectFull: Statistical smoothing
        Type: general
      – SubjectFull: Telegraph & telegraphy
        Type: general
      – SubjectFull: Equations
        Type: general
    Titles:
      – TitleFull: Summation Method for Fourier Series Associated with a Mixed Problem for the Inhomogeneous Telegraph Equation.
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              Text: Mar2025
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              Y: 2025
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