Abstract
We study the application of certain spline collocation methods to Volterra integro-differential equations of orderr where ther-th order derivative of the unknown solution occurs also in the kernel of the integral term. The analysis focuses on the question of the optimal discrete convergence order (at the knots of the approximating spline function).
Zusammenfassung
Diese Arbeit behandelt die numerische Lösung von Volterraschen Integrodifferential-gleichungenr-ter Ordnung, deren Kernfunktion dier-te Ableitung der gesuchten Lösung enthält, mittels Spline-Funktionen. In Mittelpunkt der Arbeit steht die Frage der optimalen diskreten Konvergenzordnung an den Knoten der approximierenden Spline-Funktion.
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This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC Grant No. A9406).
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Brunner, H. The approximate solution of initial-value problems for general Volterra integro-differential equations. Computing 40, 125–137 (1988). https://doi.org/10.1007/BF02247941
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DOI: https://doi.org/10.1007/BF02247941