Volume 60, pp. 136-168, 2024.

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

Bailey Rester, Anzhelika Vasilyeva, and James V. Lambers

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.

Full Text (PDF) [682 KB], BibTeX

Key words

spectral methods, wave equation, convergence analysis, variable coefficients

AMS subject classifications

65M70, 65M12, 65F60

Links to the cited ETNA articles

[23]	Vol. 28 (2007-2008), pp. 114-135 James V. Lambers: Derivation of high-order spectral methods for time-dependent PDE using modified moments
[24]	Vol. 31 (2008), pp. 86-109 James V. Lambers: Enhancement of Krylov subspace spectral methods by block Lanczos iteration

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