Two-derivative Runge-Kutta-Nyström methods for second-order ordinary differential equations

2015 ◽  
Vol 70 (4) ◽  
pp. 897-927 ◽  
Author(s):  
Zhaoxia Chen ◽  
Zeyu Qiu ◽  
Juan Li ◽  
Xiong You
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Nyström Methods ◽  
Runge Kutta

scholarly journals High order explicit Runge-Kutta pairs for ephemerides of the Solar System and the Moon

2000 ◽  
Vol 4 (2) ◽  
pp. 183-192 ◽  
Author(s):  
Philip W. Sharp
Keyword(s):  
Solar System ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Test Problem ◽  
Second Order ◽  
High Order ◽  
The Moon ◽  
Initial Value ◽  
New Family ◽  
Runge Kutta

Numerically integrated ephemerides of the Solar System and the Moon require very accurate integrations of systems of second order ordinary differential equations. We present a new family of 8-9 explicit Runge-Kutta pairs and assess the performance of two new 8-9 pairs on the equations used to create the ephemeris DE102. Part of this work is the introduction of these equations as a test problem for integrators of initial value ordinary differential equations.

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