Trigonometrically Fitted Block Backward Differentiation Methods for First Order Initial Value Problems with Periodic Solution

A family of Trigonometrically Fitted Backward Differentiation Formula (TBDF) whose coefficients depend on the frequency and step size for periodic initial value problems is presented. The method is constructed based on collocation techniques. The primary method of TBDF is obtained from its continuous version while the additional methods are derived from the derivative of the continuous version which are combined and applied in block form as simultaneous numerical integrators. The stability properties of the method are discussed and numerical experiments show that the TBDF is an accurate numerical integrator.