Construction of L stable second derivative trigonometrically fitted block backward differentiation formula for the solution of oscillatory initial value problems

Abstract

A second derivative trigonometrically fitted block backward differentiation formula (SDTFBBDF) based on the collocation technique is proposed in this paper. The method is specifically considered for the numerical solution of oscillatory problems. The SDTFBBDF which has one main method and one complementary method as by-products of the continuous second derivative backward differentiation formula (CSDBDF) whose coefficients depend on the frequency and step size. The stability and the convergence of SDTFBBDF are established and the performance of the proposed method is verified on some numerical examples to show its accuracy and efficiency.