Two Step Trigonometrically Fitted Method for Numerical Solution of Initial Value Problems with Oscillating Solutions

A continuous two-step method using trigonometric function basis is developed and used to produce two discrete methods which are simultaneously applied as numerical integrators by assembling them into a block method with trigonometric basis for solving oscillatory initial value problems(IVP). The stability property of the method is well discussed and the performance of the method is demonstrated on some numerical examples to show accuracy and effciency advantages.