scholarly journals Third-order explicit two-step Runge-Kutta-Nyström method for solving second-order ordinary differential equations

2013 ◽  
Author(s):  
Latifah Md Ariffin ◽  
Norazak Senu ◽  
Mohamed Suleiman
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Third Order ◽  
Runge Kutta

scholarly journals INTEGRATION FOR SPECIAL THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS USING IMPROVED RUNGE-KUTTA DIRECT METHOD

2015 ◽  
Vol 34 (2) ◽  
pp. 172-179 ◽  
Author(s):  
Kasim Abbas Hussain ◽  
Fudziah Ismail ◽  
Norazak Senu ◽  
Faranak Rabiei ◽  
Rabha Ibrahim
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Direct Method ◽  
Third Order ◽  
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.

scholarly journals New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPs

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Norazak Senu ◽  
Mohamed Suleiman ◽  
Fudziah Ismail ◽  
Norihan Md Arifin
Keyword(s):  
Differential Equations ◽  
Truncation Error ◽  
Second Order ◽  
Phase Lag ◽  
Initial Value ◽  
Third Order ◽  
Second Order Differential Equations ◽  
New Methods ◽  
Oscillating Solutions ◽  
Runge Kutta

New 4(3) pairs Diagonally Implicit Runge-Kutta-Nyström (DIRKN) methods with reduced phase-lag are developed for the integration of initial value problems for second-order ordinary differential equations possessing oscillating solutions. Two DIRKN pairs which are three- and four-stage with high order of dispersion embedded with the third-order formula for the estimation of the local truncation error. These new methods are more efficient when compared with current methods of similar type and with the L-stable Runge-Kutta pair derived by Butcher and Chen (2000) for the numerical integration of second-order differential equations with periodic solutions.

Sign in / Sign up

Export Citation Format

Share Document