Block Trigonometrically Fitted Backward Differentiation Formula for the Initial Value Problem with Oscillating Solutions

Abstract

This paper presents a fitted backward differentiation formula (BTBDF) whose coefficients are functions of a fixed fitting frequency and step length especially designed for the numerical integration of first-order Initial Value Problems (IVPs) with oscillatory results. The BTBDF is a product of three discrete formulas which are obtained from a continuous second derivative trigonometrically fitted method (CSDTFM). The BTBDF is applied in a block-wise form that makes it enjoys the advantages of the self-starting formula. The convergence of the BTBDF is discussed and its superiority is demonstrated in some numerical experiments to illustrate accuracy advantage.