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 Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.: Year: Volume: Issue: Page: Find

 Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2019, Volume 19, Issue 3, Pages 280–288 (Mi isu807)

Scientific Part
Mathematics

On classic solution of the problem for a homogeneous wave equation with fixed end-points and zero initial velocity

A. P. Khromov

Saratov State University, 83 Astrakhanskaya St., Saratov 410012, Russia

Abstract: The paper gives necessary and sufficient conditions of classic solution for a homogeneous wave equation with a summable potential, fixed end-point, and zero initial velocity. With the use of Fourier method and Krylov method of improving series rate convergence an analogue of d'Alembert formula is derived in the form of exponentially convergent series. The paper essentially supports and extends the results of our work carried out in 2016. The suggested new method, based on the use of divergent (in Euler's sense) series, is very economical in using well-known mathematical facts. It opens a perspective of considerable advancement in studying other boundary problems for partial differential equations.

Key words: Fourier method, divergent series, Krylov method, classic solution, resolvent.

DOI: https://doi.org/10.18500/1816-9791-2019-19-3-280-288

Full text: PDF file (189 kB)

Bibliographic databases:

UDC: 517.96:517.984
Accepted:04.06.2019

Citation: A. P. Khromov, “On classic solution of the problem for a homogeneous wave equation with fixed end-points and zero initial velocity”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 19:3 (2019), 280–288

Citation in format AMSBIB
\Bibitem{Khr19} \by A.~P.~Khromov \paper On classic solution of the problem for a homogeneous wave equation with fixed end-points and zero initial velocity \jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform. \yr 2019 \vol 19 \issue 3 \pages 280--288 \mathnet{http://mi.mathnet.ru/isu807} \crossref{https://doi.org/10.18500/1816-9791-2019-19-3-280-288} \elib{http://elibrary.ru/item.asp?id=39542330}