Semi implicit hybrid methods with higher order dispersion for solving oscillatory problems

• Main Authors: Ahmad, Sufia Zulfa, Ismail, Fudziah, Senu, Norazak, Suleiman, Mohamed
• Format: Article
• Language: English
• Published: Hindawi Publishing Corporation 2013
• Online Access: http://psasir.upm.edu.my/id/eprint/30209/1/30209.pdf; http://psasir.upm.edu.my/id/eprint/30209/; https://www.hindawi.com/journals/aaa/2013/136961/abs/

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.