An optimized Runge-Kutta method for the solution of orbital problems
By Zacharias A. Anastassi, T. E. Simos. 2005
185 citations recorded by the source corpus.
We present a new explicit Runge-Kutta method with algebraic order four, minimum error of the fifth algebraic order (the limit of the error is zero, when the step-size tends to zero), infinite order of dispersion and eighth order of dissipation. The efficiency of the newly constructed method is shown through the numerical results of a wide range of methods when these are applied to well-known periodic orbital problems.
Subfields: Computational Theory and Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/65fbc0021a3b4fdfdf5cd239fa33675928e9afd7
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In Computational Theory and Mathematics
- Ibraheem Alolyan
- Ke Yan
- T. E. Simos
- Charalambos Tsitouras
- Kenan Mu
- Jing Ma
- Zacharias A. Anastassi
- Athinoula Kosti
In Numerical Analysis
- Ibraheem Alolyan
- Ke Yan
- T. E. Simos
- Charalambos Tsitouras
- Kenan Mu
- Athinoula Kosti
- Zacharias A. Anastassi
- Jing Ma
Citations in the corpus
- High algebraic order methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation (2010, methodology): “In [ 30 ] an Explicit Runge-Kutta method with algebraic order four, infinite order of phase-lag and eighth order of amplification error for the solution of well-known periodicorbitalproblems.Applicationofthenewdevelopedmethodtothewellknown orbital problems shows the efficiency of the method.”
- A finite difference pair with improved phase and stability properties (2017, methodology): “of Runge-Kutta and of Runge-Kutta Nyström type) with minimal phase-lag (see [35,38,56, 59]) – Exponentially and trigonometrically fitted Runge-Kutta and RungeKutta Nyström algorithms (see [62–66,83,84,93]) – Multistep phase-fitted methods, phase-lag derivatives fitted and multistep methods with mini”