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We constructed three two-step semi-implicit hybridmethods (SIHMs) for solving oscillatory second order ordinary differential equations (ODEs). The first two methods are three-stage fourth-order and three-stage fifth-order with dispersion order six and zero dissipation. The third is a four-stage fifth-order method with dispersion order eight and dissipation order five. Numerical results show that SIHMs are more accurate as compared to theexisting hybrid methods, Runge-Kutta Nyström (RKN) and Runge-Kutta (RK)methods of the same order and Diagonally Implicit Runge-Kutta Nyström(DIRKN) method of the same stage. The intervals of absolute stability or periodicity ofSIHM for ODE are also presented

Semi Implicit Hybrid Methods with Higher Order Dispersion for Solving Oscillatory Problems