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

Sufia Zulfa Ahmad | Zendy; Fudziah Ismail | Zendy; Norazak Senu | Zendy; Mohamed Suleiman | Zendy

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

Author(s) -

Sufia Zulfa Ahmad,

Fudziah Ismail,

Norazak Senu,

Mohamed Suleiman

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/136961

Subject(s) - runge–kutta methods , mathematics , ode , ordinary differential equation , dispersion (optics) , dissipation , stability (learning theory) , explicit and implicit methods , order (exchange) , l stability , numerical methods for ordinary differential equations , diagonal , mathematical analysis , differential equation , geometry , differential algebraic equation , thermodynamics , physics , finance , machine learning , computer science , optics , economics

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

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