A two-step trigonometrically fitted semi-implicit hybrid method for solving special second order oscillatory differential equation

In this paper,we derived a semi-implicit hybrid method (sihm) which is a two-step method to solve special second order ordinary differential equations (odes). the sihm which is three-stage and fourth-order is then trigonometrically fitted and denoted by tf-sihm3(4). the method is constructed using trigonometrically fitted properties instead of using phase-lag and amplification properties. numerical integration show that tf-sihm3(4) is more accurate in term of accuracy compared to the existing explicit and implicit methods of the same order.