Complementary Lidstone Interpolation and Boundary Value Problems. (29th December 2009)

• Record Type: Journal Article
• Authors: Agarwal, Ravi P.; Pinelas, Sandra; Wong, Patricia J. Y.
• Other Names: O'Regan Donal Academic Editor.
• Is Part Of: Journal of inequalities and applications. Volume 2009(2009)
• Publication Date: 2009-12-29
• Subjects: Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/2009/624631
• Languages: English
• ISSNs: 1029-242X

Abstract

Abstract : We shall introduce and construct explicitly the complementary Lidstone interpolating polynomialP 2 m ( t ) of degree2 m, which involves interpolating data at the odd-order derivatives. ForP 2 m ( t ) we will provide explicit representation of the error function, best possible error inequalities, best possible criterion for the convergence of complementary Lidstone series, and a quadrature formula with best possible error bound. Then, these results will be used to establish existence and uniqueness criteria, and the convergence of Picard's, approximate Picard's, quasilinearization, and approximate quasilinearization iterative methods for the complementary Lidstone boundary value problems which consist of a( 2 m + 1 ) th order differential equation and the complementary Lidstone boundary conditions.