New Phase-Fitted and Amplification-Fitted Fourth-Order and Fifth-Order Runge-Kutta-Nyström Methods for Oscillatory Problems. (9th October 2013)

• Record Type: Journal Article
• Authors: Moo, K. W.; Senu, N.; Ismail, F.; Suleiman, M.
• Other Names: Vigo-Aguiar Jesus Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-10-09
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/939367
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : Two new Runge-Kutta-Nyström (RKN) methods are constructed for solving second-order differential equations with oscillatory solutions. These two new methods are constructed based on two existing RKN methods. Firstly, a three-stage fourth-order Garcia's RKN method. Another method is Hairer's RKN method of four-stage fifth-order. Both new derived methods have two variable coefficients with phase-lag of order infinity and zero amplification error (zero dissipative). Numerical tests are performed and the results show that the new methods are more accurate than the other methods in the literature.