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Journal of Applied Mathematics
Volume 2015 (2015), Article ID 343295, 17 pages
http://dx.doi.org/10.1155/2015/343295
Research Article

A Family of Trigonometrically Fitted Enright Second Derivative Methods for Stiff and Oscillatory Initial Value Problems

1Department of Mathematics, USC Salkehatchie, Walterboro, SC 29488, USA
2Department of Mathematics and Statistics, Austin Peay State University, Clarksville, TN 37044, USA

Received 23 January 2015; Accepted 23 April 2015

Academic Editor: Mehmet Sezer

Copyright © 2015 F. F. Ngwane and S. N. Jator. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A family of Enright’s second derivative formulas with trigonometric basis functions is derived using multistep collocation method. The continuous schemes obtained are used to generate complementary methods. The stability properties of the methods are discussed. The methods which can be applied in predictor-corrector form are implemented in block form as simultaneous numerical integrators over nonoverlapping intervals. Numerical results obtained using the proposed block form reveal that the new methods are efficient and highly competitive with existing methods in the literature.