Numerical quadrature based on an exponential type of interpolation
- 1 January 1991
- journal article
- research article
- Published by Taylor & Francis in International Journal of Computer Mathematics
- Vol. 38 (3-4) , 193-209
- https://doi.org/10.1080/00207169108803969
Abstract
It is shown that a function f(x) can be approximated in a unique way by a function so that f n (x) and f(x) coincide in at least (n + 1) equidistant points. Several equivalent expressions of the interpolation function f n (x) of exponential type are given, and the error term is derived in closed form. With this type of interpolation a set of modified Newton-Cotes quadrature rules of the closed and of the open type are established. The total truncation error for these rules is discussed. Numerical examples show the efficiency of the modified rules and exhibit the particular advantage that can be taken of the explicit form of the error term.Keywords
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- Families of backward differentiation methods based on a new type of mixed interpolationComputers & Mathematics with Applications, 1990
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