Stability analysis of frequency and step length dependent Runge–Kutta–Nyström methods

2006 ◽  
Vol 22 (4) ◽  
pp. 395-402 ◽  
Author(s):  
M. Carpentieri ◽  
B. Paternoster
Keyword(s):  
Stability Analysis ◽  
Step Length ◽  
Nyström Methods ◽  
Runge Kutta

scholarly journals A Phase-Fitted and Amplification-Fitted Explicit Runge–Kutta–Nyström Pair for Oscillating Systems

2021 ◽  
Vol 26 (3) ◽  
pp. 59
Author(s):  
Musa Ahmed Demba ◽  
Higinio Ramos ◽  
Poom Kumam ◽  
Wiboonsak Watthayu
Keyword(s):  
Stability Analysis ◽  
Numerical Experiments ◽  
Order Of Convergence ◽  
Truncation Error ◽  
Local Truncation Error ◽  
Nyström Methods ◽  
Oscillating Systems ◽  
The Common ◽  
Runge Kutta ◽  
The Stability

An optimized embedded 5(3) pair of explicit Runge–Kutta–Nyström methods with four stages using phase-fitted and amplification-fitted techniques is developed in this paper. The new adapted pair can exactly integrate (except round-off errors) the common test: y″=−w2y. The local truncation error of the new method is derived, and we show that the order of convergence is maintained. The stability analysis is addressed, and we demonstrate that the developed method is absolutely stable, and thus appropriate for solving stiff problems. The numerical experiments show a better performance of the new embedded pair in comparison with other existing RKN pairs of similar characteristics.

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