Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9509489 | Journal of Computational and Applied Mathematics | 2005 | 14 Pages |
Abstract
For a function fâC2n+1a,b an explicit polynomial interpolant in a and in the even derivatives up to the order 2n-1 at the end-points of the interval is derived. Explicit Cauchy and Peano representations and bounds for the error are given and the analysis of the remainder term allows to find sufficient conditions on f so that the polynomial approximant converges to f. These results are applied to derive a new summation formula with application to rectangular quadrature rule. The polynomial interpolant is related to a fairly interesting boundary value problem for ODEs. We will exhibit solutions for this problem in some special situations.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
F.A. Costabile, F. Dell'Accio, R. Luceri,