SERK2v2: A new second-order stabilized explicit Runge-Kutta method for stiff problems

2012 ◽  
Vol 29 (1) ◽  
pp. 170-185 ◽  
Author(s):  
B. Kleefeld ◽  
J. Martín-Vaquero
Keyword(s):  
Second Order ◽  
Stiff Problems ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta

Symmetric and symplectic methods for gyrocenter dynamics in time-independent magnetic fields

2016 ◽  
Vol 07 (02) ◽  
pp. 1650008 ◽  
Author(s):  
Beibei Zhu ◽  
Zhenxuan Hu ◽  
Yifa Tang ◽  
Ruili Zhang
Keyword(s):  
Numerical Simulation ◽  
Hamiltonian System ◽  
Second Order ◽  
Symplectic Methods ◽  
Kutta Method ◽  
Numerical Accuracy ◽  
Runge Kutta Method ◽  
Simulation Results ◽  
Runge Kutta

We apply a second-order symmetric Runge–Kutta method and a second-order symplectic Runge–Kutta method directly to the gyrocenter dynamics which can be expressed as a noncanonical Hamiltonian system. The numerical simulation results show the overwhelming superiorities of the two methods over a higher order nonsymmetric nonsymplectic Runge–Kutta method in long-term numerical accuracy and near energy conservation. Furthermore, they are much faster than the midpoint rule applied to the canonicalized system to reach given precision.

An efficient implicit Runge–Kutta method for second order systems

2006 ◽  
Vol 178 (2) ◽  
pp. 229-238 ◽  
Author(s):  
Basem S. Attili ◽  
Khalid Furati ◽  
Muhammed I. Syam
Keyword(s):  
Second Order ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Second Order Systems

scholarly journals Analysis of linear and nonlinear stiff problems using the RK-Butcher algorithm

2006 ◽  
Vol 2006 ◽  
pp. 1-15 ◽  
Author(s):  
S. Sekar
Keyword(s):  
Exact Solutions ◽  
Numerical Solution ◽  
Arithmetic Mean ◽  
Stiff Problems ◽  
Graphical Form ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Linear And Nonlinear ◽  
Runge Kutta

I present a numerical solution of linear and nonlinear stiff problems using the RK-Butcher algorithm. The obtained discrete solutions using the RK-Butcher algorithm are found to be very accurate and are compared with the exact solutions of the linear and nonlinear stiff problems and also with the Runge-Kutta method based on arithmetic mean (RKAM). A topic of stability for the RK-Butcher algorithm is discussed in detail. Error graphs for discrete and exact solutions are presented in a graphical form to show the efficiency of the RK-Butcher algorithm. The results obtained show that RK-Butcher algorithm is more useful for solving linear and nonlinear stiff problems and the solution can be obtained for any length of time.

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