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

Abstract EN

We constructed three two-step semi-implicit hybrid methods (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 the existing 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 of SIHM for ODE are also presented.