A trigonometrically adapted 6(4) explicit Runge–Kutta–Nyström pair to solve oscillating systems. (3rd July 2022)

• Record Type: Journal Article
• Authors: Demba, Musa Ahmed; Ramos, Higinio; Kumam, Poom; Watthayu, Wiboonsak; Senu, Norazak; Ahmed, Idris
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 1(2023)
• Page Start: 560
• Page End: 578
• Publication Date: 2022-07-03
• Subjects: initial value problems -- oscillatory problems -- Runge–Kutta–Nyström pair -- trigonometrically fitted approach; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8528
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this study, a trigonometrically adapted 6(4) explicit Runge–Kutta–Nyström (RKN) pair with six stages is formulated, considering a previous method developed by El‐Mikkawy and Rahmo. The obtained adapted pair integrates exactly the usual test equation: y ′ ′ = − w 2 y $$ {y}^{\prime \prime }=-{w}^2y $$ . The local truncation error of the new method is presented, showing that the algebraic order of the original method is maintained. The periodicity interval of the new method is computed, showing that the developed method is "almost" P‐stable. The numerical examples considered clearly show the superiority of the new developed embedded pair over other RKN methods of algebraic orders 6(4) with six stages appeared in the literature.