A SIMPSON TYPE TRIGONOMETRICALLY FITTED BLOCK SCHEME FOR NUMERICAL INTEGRATION OF OSCILLATORY PROBLEMS

Abstract

_{The construction of Second Derivative Trigonometrically Fitted Block Scheme of Simpson Type (TFBSST) of algebraic order 6via collocation techniques is considered for the solution of oscillatory problems. A Continuous Second Derivative Trigonometrically Fitted method (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 investigation of the stability properties of the method shows that the method is zero stable, consistent and convergent. Numerical examples presented show that the method is accurate and efficient}