Abstract
In two papers Holyhead et al. (1975, 1976) analyzed the convergence of general linear multistep methods under minimum continuity assumptions. This paper is concerned with determining the maximum orders of convergence of these methods given that the truncation error has an asymptotic expansion with sufficiently many terms.
Zusammenfassung
Die Konvergenzeigenschaften von linearen Mehrschrittverfahren für Volterrasche Integralgleichungen erster Art mit minimalen Stetigkeitsbedingungen wurden in zwei Arbeiten von Holyhead et al. (1975, 1976) analysiert. Die vorliegende Arbeit beschäftigt sich, unter der Voraussetzung, daß der Diskretisierungsfehler eine hinreichende asymptotische Entwicklung besitzt, mit der Frage nach der maximalen Konvergenzordnung.
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McKee, S. Best convergence rates of linear multistep methods for Volterra first kind equations. Computing 21, 343–358 (1979). https://doi.org/10.1007/BF02248734
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DOI: https://doi.org/10.1007/BF02248734