New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPs
This article is part of Special Issue:
Norazak Senu,
Mohamed Suleiman,
Fudziah Ismail,
Norihan Md Arifin,
Corresponding Author
Norazak Senu
Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia upm.edu.my
Search for more papers by this authorMohamed Suleiman
Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia upm.edu.my
Search for more papers by this authorFudziah Ismail
Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia upm.edu.my
Search for more papers by this authorNorihan Md Arifin
Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia upm.edu.my
Search for more papers by this authorNorazak Senu,
Mohamed Suleiman,
Fudziah Ismail,
Norihan Md Arifin,
Corresponding Author
Norazak Senu
Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia upm.edu.my
Search for more papers by this authorMohamed Suleiman
Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia upm.edu.my
Search for more papers by this authorFudziah Ismail
Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia upm.edu.my
Search for more papers by this authorNorihan Md Arifin
Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia upm.edu.my
Search for more papers by this authorAcademic Editor: Taher S. Hassan
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.
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