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A Phase- and Amplification-Fitted 5(4) Diagonally Implicit Runge–Kutta–Nyström Pair for Oscillatory Systems.
- Source :
-
Bulletin of the Iranian Mathematical Society . Jun2023, Vol. 49 Issue 3, p1-23. 23p. - Publication Year :
- 2023
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10186301
- Volume :
- 49
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Bulletin of the Iranian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 162985229
- Full Text :
- https://doi.org/10.1007/s41980-023-00765-9