Construction of exponentially fitted symplectic Runge-Kutta-Nyström methods from partitioned Runge-Kutta methods

2014 ◽  
Author(s):  
Theodore Monovasilis ◽  
Zacharoula Kalogiratou ◽  
T. E. Simos
Keyword(s):  
Nyström Methods ◽  
Exponentially Fitted ◽  
Runge Kutta

scholarly journals Embedded Exponentially-Fitted Explicit Runge-Kutta-Nyström Methods for Solving Periodic Problems

Computation ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 32
Author(s):  
Musa Demba ◽  
Poom Kumam ◽  
Wiboonsak Watthayu ◽  
Pawicha Phairatchatniyom
Keyword(s):  
Error Estimation ◽  
Variable Step Size ◽  
Local Error ◽  
Step Size ◽  
Local Error Estimation ◽  
Nyström Methods ◽  
Periodic Problems ◽  
Variable Step ◽  
Exponentially Fitted ◽  
Runge Kutta

In this work, a pair of embedded explicit exponentially-fitted Runge–Kutta–Nyström methods is formulated for solving special second-order ordinary differential equations (ODEs) with periodic solutions. A variable step-size technique is used for the derivation of the 5(3) embedded pair, which provides a cheap local error estimation. The numerical results obtained signify that the new adapted method is more efficient and accurate compared with the existing methods.

scholarly journals Revised exponentially fitted Runge–Kutta–Nyström methods

2014 ◽  
Vol 30 ◽  
pp. 56-60 ◽  
Author(s):  
R. D’Ambrosio ◽  
B. Paternoster ◽  
G. Santomauro
Keyword(s):  
Nyström Methods ◽  
Exponentially Fitted ◽  
Runge Kutta
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