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

S. Z. Ahmad, F. Ismail, N. Senu and M. Suleiman

Abstract and Applied Analysis, 2013, vol. 2013, 1-10

Abstract:

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:136961

DOI: 10.1155/2013/136961

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