Maximal Order Block Trigonometrically Fitted Scheme for the Numerical Treatment of Second Order Initial Value Problem with Oscillating Solutions

Abstract

A Maximal Order Block Trigonometrically Fitted Method (MBTFM) whose coefficients are functions of frequency and step size specially designed for the solution of second order Initial Value Problems (IVPs) with oscillatory solution is proposed in this paper. The MBTFM is obtained from one discrete formulae with two complementary formula which are provided by Continuous Trigonometrically Fitted Block Method (CTFBM). The convergence of the MBTFM is discussed and the performance of the method is demonstrated on some numerical examples to show accuracy and efficiency of the method.