On the multistep time discretization of linear\newline initial-boundary value problems and their boundary integral equations (original) (raw)
Summary.
Convergence estimates in terms of the data are shown for multistep methods applied to non-homogeneous linear initial-boundary value problems. Similar error bounds are derived for a new class of time-discrete and fully discrete approximation schemes for boundary integral equations of such problems, e.g., for the single-layer potential equation of the wave equation. In both cases, the results are obtained from convergence and stability estimates for operational quadrature approximations of convolutions. These estimates, which are also proved here, depend on bounds of the Laplace transform of the (distributional) convolution kernel outside the stability region scaled by the time stepsize, and on the smoothness of the data.
Access this article
Subscribe and save
- Starting from 10 chapters or articles per month
- Access and download chapters and articles from more than 300k books and 2,500 journals
- Cancel anytime View plans
Buy Now
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
Instant access to the full article PDF.
Similar content being viewed by others
Author information
Authors and Affiliations
- Institut f\"ur Angewandte Mathematik und Statistik, Universit\"at W\"urzburg, Am Hubland, D-97074 W\"urzburg, Germany , , , , , , DE
Ch. Lubich
Additional information
Received January 18, 1993 / Revised version received September 15, 1993
Rights and permissions
About this article
Cite this article
Lubich, C. On the multistep time discretization of linear\newline initial-boundary value problems and their boundary integral equations .Numer. Math. 67, 365–389 (1994). https://doi.org/10.1007/s002110050033
- Issue date: April 1994
- DOI: https://doi.org/10.1007/s002110050033