Abstract
Padé or Obrechkoff methods based on diagonal or subdiagonal Padé approximations for the exponential function combine high accuracy and good stability; but the occurrence of higher derivatives makes their efficient implementation difficult. For the 3rd order subdiagonal 2nd derivative method, we have found an implementation which has resulted in a competitive code for moderately large, strongly stiff systems, under moderate accuracy requirements.
Zusammenfassung
Die Padé- oder Obrechkoff-Verfahren, die auf diagonalen oder subdiagonalen Padé-Approximationen der Exponentialfunktion beruhen, vereinen hohe Genauigkeit mit guter Stabilität; wegen des Auftretens höherer Ableitungen sind sie aber nur schwer effizient zu implementieren. Für das subdiagonale Verfahren dritter Ordnung mit zweiten Ableitungen haben wir eine Implementierung gefunden, die zu einem Code geführt hat, der für nicht besonders große, stark steife Systeme bei mäßigen Genauigkeitsforderungen konkurrenzfähig mit gängigen Codes ist.
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Hlynsky, Y., Panchyshyn, Y. Efficient implementation of a 2nd derivative method for stiff ODEs. Computing 53, 95–99 (1994). https://doi.org/10.1007/BF02262110
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DOI: https://doi.org/10.1007/BF02262110