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