An extended doubly-adaptive quadrature method based on the by Hasegawa T., Hibino S., Hosoda Y.

By Hasegawa T., Hibino S., Hosoda Y.

Summary An development is made to an automated quadrature as a result of Ninomiya (J. Inf. procedure. 3:162–170, 1980) of adaptive sort in accordance with the Newton–Cotes rule via incorporating a doubly-adaptive set of rules as a result of Favati, Lotti and Romani (ACM Trans. Math. Softw. 17:207–217, 1991; ACM Trans. Math. Softw. 17:218–232, 1991). We evaluate the current process in functionality with a few others through the use of numerous attempt difficulties together with Kahaner’s ones (Computation of numerical quadrature formulation. In: Rice, J.R. (ed.) Mathematical software program, 229–259. educational, Orlando, FL, 1971).Keywords computerized quadrature · Adaptive set of rules · Numerical comparability

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1978,88, 22 514). A. V. Anisimov, V. F. Ionova, andE. A. Viktorova, Zhur. org. , 1977, 13, 2624. '21 The (242) (243) W. E. Truce, B. VanGemert, and W. W. Brand, J. Org. , 1978,43,101. W . MacDowell and F. L. Ballas, J. Org. Chem. 1977,42,3717. lZ3 lZs M. Novi, F. Sancassan, G. Guanti. C. Dell'Erba, and G. Leandri, Chimica e Industria, 1977,59,299. H. Herrmann, and G. A. Hoyer, Chem. , 1978,111,770. K. Kobayashi and K. Mutai, Chem. Letters, 1977,1149. l~~ Unlike open-chain a@-unsaturatedsulphones, it does not form the corresponding epoxide when treated with hydroperoxide anion, but instead yields the ketone (254); 3-substituted benzothiophen dioxides (253; R = Me, Et, or Ph) give alcohols (255) in this r e a ~ t i 0 n .

Rodionova, and A. A. Petrov, Zhur. org. , 1977, 13, 1564. V. G . Lendel, Yu. V. Migalina, S. V. Galla, A. S. KoLmin, and N. S. Zefirov, Khim. geterotsikl. Soedinenii, 1977, 1340. G . Marechal, L. Christiaens, M. Renson, P. Jacquignon, and A. Croisy, Bull. chim. France, 1977, 157. T. Frejd, Chemica Scripta, 1976, 10, 133. Tran Quang Minh, L. Christiaens, P. Grandclaudon, and A. Lablache-Combier, Tetrahedron, 1977, 33. 2225. r. r. -Formation. ) has been prepared by the action of o, TosylCHMeNC H (279) (280) Mfl Me CN N H (281) H (282) malononitrile on the acetamido-ketones AcNHCHRCOMe.

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