Title of article :
A Phase- and Amplification-Fitted 5(4) Diagonally Implicit Runge–Kutta–Nyström Pair for Oscillatory Systems
Author/Authors :
Ahmed Demba ، Musa Department of Mathematics - Faculty of Science - King Mongkut’s University of TechnologyThonburi (KMUTT) , Senu ، Norazak Department of Mathematics Statistics and Institute for Mathematical Research - Faculty of Science - Universiti Putra Malaysia , Ramos ، Higinio Department of Applied Mathematics - Faculty of Sciences - University of Salamanca , Kumam ، Poom Department of Mathematics - Faculty of Science - King Mongkut’s University of TechnologyThonburi (KMUTT) , Watthayu ، Wiboonsak Department of Mathematics - Faculty of Science - King Mongkut’s University of TechnologyThonburi (KMUTT)
Abstract :
In this work, a phase- and amplification-fitted 5(4) diagonally implicit pair of Runge– Kutta–Nyström methods with four stages is developed to solve special second-order ordinary differential equations (ODEs), whose solutions are oscillatory. The local truncation errors of the formulas of the new pair are given, showing that the orders are maintained, with respect to the original formulas. The stability of the new method is studied, showing that the developed formulas present non-vanishing intervals of absolute stability. The numerical examples considered clearly show the robustness of the developed embedded pair over other diagonally implicit Runge–Kutta–Nyström (DIRKN) pairs in the literature.
Keywords :
Phase , fitted and amplification , fitted approach , Diagonally implicit methods , Embedded Pairs , Runge–Kutta–Nyström methods , Oscillatory system , Initial value problems ,
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
