On a family of trigonometrically fitted extended backward differentiation formulas for stiff and oscillatory initial value problems

Abstract

A Class of Continuous Extended Backward Differentiation Formula using Trigonometric Basis functions (CEBDTB) with one superfuture point is constructed and used to generate a family of Trigonometrically Fitted Extended Backward Differentiation Formula (TFEBDF) and other discrete methods as by-products. This family of discrete schemes together with the TFEBDF are simultaneously applied as numerical integrators by assembling them into a Block Trigonometrically Fitted Extended Backward Differentiation Method (BTFEBDM). The error analysis, stability properties, and implementation of the BTFEBDM are discussed, and the class of methods is shown to be suitable for oscillatory and/or stiff Initial Value Problems (IVPs). The performance of the method is demonstrated on some numerical examples to show its accuracy and computational efficiency.