Integration formulas and schemes based on -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 | References | Similar Articles | Additional Information

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 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