• Ronny Ramlau, Lothar Reichel (Hg.)

ETNA - Electronic Transactions on Numerical Analysis

Bild


Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.

Verlag der Österreichischen Akademie der Wissenschaften
Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400
https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at

Bestellung/Order


Bild
ETNA - Electronic Transactions on Numerical Analysis



ISBN 978-3-7001-8258-0
Online Edition



Send or fax to your local bookseller or to:

Verlag der Österreichischen Akademie der Wissenschaften
Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2,
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400
https://verlag.oeaw.ac.at, e-mail: bestellung.verlag@oeaw.ac.at
UID-Nr.: ATU 16251605, FN 71839x Handelsgericht Wien, DVR: 0096385

Bitte senden Sie mir
Please send me
 
Exemplar(e) der genannten Publikation
copy(ies) of the publication overleaf


NAME


ADRESSE / ADDRESS


ORT / CITY


LAND / COUNTRY


ZAHLUNGSMETHODE / METHOD OF PAYMENT
    Visa     Euro / Master     American Express


NUMMER

Ablaufdatum / Expiry date:  

    I will send a cheque           Vorausrechnung / Send me a proforma invoice
 
DATUM, UNTERSCHRIFT / DATE, SIGNATURE

BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
Bild

Convergence analysis of a Krylov subspace spectral method for the 1D wave equation in an inhomogeneous medium

    Bailey Rester, Anzhelika Vasilyeva, James V. Lambers

ETNA - Electronic Transactions on Numerical Analysis, pp. 136-168, 2024/04/03

doi: 10.1553/etna_vol60s136

doi: 10.1553/etna_vol60s136


PDF
X
BibTEX-Export:

X
EndNote/Zotero-Export:

X
RIS-Export:

X 
Researchgate-Export (COinS)

Permanent QR-Code

doi:10.1553/etna_vol60s136



doi:10.1553/etna_vol60s136

Abstract

This paper presents a convergence analysis of a Krylov subspace spectral (KSS) method applied to an 1D wave equation in an inhomogeneous medium. It will be shown that for sufficiently regular initial data, this KSS method yields unconditional stability, spectral accuracy in space, and second-order accuracy in time in the case of constant wave speed and a bandlimited reaction term coefficient. Numerical experiments that corroborate the established theory are included along with an investigation of generalizations, such as to higher space dimensions and nonlinear PDEs, that features performance comparisons with other Krylov subspace-based time-stepping methods. This paper also includes the first stability analysis of a KSS method that does not assume a bandlimited reaction term coefficient.

Keywords: spectral methods, wave equation, convergence analysis, variable coefficients