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

Ahmad, Sufia Zulfa and Ismail, Fudziah and Senu, Norazak and Suleiman, Mohamed (2013) Semi implicit hybrid methods with higher order dispersion for solving oscillatory problems. Abstract and Applied Analysis, 2013 . art. no. 136961. pp. 1-10. ISSN 1085-3375; ESSN: 1687-0409

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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.

Item Type:Article
Keyword:Dispersion; Semi-implicit; Oscillatory problems; Ordinary differential equations
Faculty or Institute:Faculty of Science
Institute for Mathematical Research
Publisher:Hindawi Publishing Corporation
DOI Number:10.1155/2013/136961
Altmetrics:http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1155/2013/136961
ID Code:30209
Deposited By: Umikalthom Abdullah
Deposited On:26 Aug 2014 15:34
Last Modified:19 Oct 2017 13:53

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