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Integration formulas and schemes based on $ g$-splines


Authors: George D. Andria, George D. Byrne and David R. Hill
Journal: Math. Comp. 27 (1973), 831-838
MSC: Primary 65D30; Secondary 65L05
DOI: https://doi.org/10.1090/S0025-5718-1973-0339460-5
MathSciNet review: 0339460
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Abstract: Numerical integration formulas of interpolatory type are generated by the integration of g-splines. These formulas, which are best in the sense of Sard, are used to construct predictor-corrector and block implicit schemes. The schemes are then compared with Adams-Bashforth-Adams-Moulton and Rosser schemes for a particular set of prototype problems. Moreover, an improved error bound for linear multistep formulas based on g-splines and a comparison of $ {L^2}$ norms of Peano kernels for Adams and natural spline formulas are given.


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DOI: https://doi.org/10.1090/S0025-5718-1973-0339460-5
Article copyright: © Copyright 1973 American Mathematical Society