An extended doubly-adaptive quadrature method based on the combination of the Ninomiya and the FLR schemes

An extended doubly-adaptive quadrature method based on the combination of the Ninomiya and the FLR schemes

An improvement is made to an automatic quadrature due to Ninomiya (J. Inf. Process. 3:162–170, 1980) of adaptive type based on the Newton–Cotes rule by incorporating a doubly-adaptive algorithm due to Favati, Lotti and Romani (ACM Trans. Math. Softw. 17:207–217, 1991; ACM Trans. Math. Softw. 17:218–...

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Veröffentlicht in:Numerical algorithms 2007-08, Vol.45 (1-4), p.101-112
Hauptverfasser: Hasegawa, Takemitsu, Hibino, Susumu, Hosoda, Yohsuke, Ninomiya, Ichizo
Format: Artikel
Sprache:eng
Schlagworte:
Adaptive algorithms
Quadratures
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Zusammenfassung:An improvement is made to an automatic quadrature due to Ninomiya (J. Inf. Process. 3:162–170, 1980) of adaptive type based on the Newton–Cotes rule by incorporating a doubly-adaptive algorithm due to Favati, Lotti and Romani (ACM Trans. Math. Softw. 17:207–217, 1991; ACM Trans. Math. Softw. 17:218–232, 1991). We compare the present method in performance with some others by using various test problems including Kahaner’s ones (Computation of numerical quadrature formulas. In: Rice, J.R. (ed.) Mathematical Software, 229–259. Academic, Orlando, FL, 1971).
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-007-9090-6