Development of an Efficient Diagonally Implicit Runge–Kutta–Nyström 5(4) Pair for Special Second Order IVPs
Musa Ahmed Demba,
Norazak Senu,
Higinio Ramos,
Wiboonsak Watthayu
Affiliations
Musa Ahmed Demba
KMUTTFixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
Norazak Senu
Department of Mathematics & Statistics and Institute for Mathematical Research, Universiti Putra Malaysia, Serdang 43400, Malaysia
Higinio Ramos
Department of Applied Mathematics, Faculty of Sciences, University of Salamanca, 37008 Salamanca, Spain
Wiboonsak Watthayu
Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
In this work, a new pair of diagonally implicit Runge–Kutta–Nyström methods with four stages is constructed. The proposed method has been derived to solve initial value problems of special second-order ordinary-differential equations. The principal local truncation error of the new method is obtained, and the main characteristics of the new method are analyzed. Some numerical experiments are performed, which demonstrate the robustness and efficiency of the new embedded pair.
