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

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 fif...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2013-01, Vol.2013 (2013), p.513-522
Main Authors: Suleiman, Mohamed bin, Senu, Norazak, Ismail, Fudzliah, Ahmad, S. Z.
Format: Article
Language:English
Subjects:
Differential equations
Mathematical research
Numerical analysis
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Summary: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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/136961