Integration formulas and schemes based on 𝑔-splines

Andria, George D.; Byrne, George D.; Hill, David R.

doi:10.1090/S0025-5718-1973-0339460-5

Integration formulas and schemes based on $g$-splines
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by George D. Andria, George D. Byrne and David R. Hill PDF

Math. Comp. 27 (1973), 831-838 Request permission

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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