New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPs

Norazak Senu, Mohamed Suleiman, Fudziah Ismail and Norihan Md Arifin

Discrete Dynamics in Nature and Society, 2012, vol. 2012, 1-20

Abstract:

New 4(3) pairs Diagonally Implicit Runge-Kutta-Nyström (DIRKN) methods with reduced phase-lag are developed for the integration of initial value problems for second-order ordinary differential equations possessing oscillating solutions. Two DIRKN pairs which are three- and four-stage with high order of dispersion embedded with the third-order formula for the estimation of the local truncation error. These new methods are more efficient when compared with current methods of similar type and with the L-stable Runge-Kutta pair derived by Butcher and Chen (2000) for the numerical integration of second-order differential equations with periodic solutions.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:324989

DOI: 10.1155/2012/324989

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