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In this paper, a L0 Stable Second Derivative Trigonometrically Fitted Block Backward Differentiation Formula of Adams Type (SDTFF) of algebraic order 4 is presented for the solution of autonomous oscillatory problems. A Continuous Second Derivative Trigonometrically Fitted (CSDTF) whose coefficients depend on the frequency and step size is constructed using trigonometric basis function. The CSDTF is used to generate the main method and one additional method which are combined and applied in block form as simultaneous numerical integrators. The stability properties of the method are investigated using boundary locus plot. It is found that the method is zero stable, consistent and hence converges. The method is applied on some numerical examples and the result show that the method is accurate and efficient.

L0 Stable Trigonometrically Fitted Block Backward Differentiation Formula of Adams Type for Autonomous Oscillatory Problems