Fifth Order Runge-Kutta-Nyström Methods with Complex Coefficients

Details Fifth Order Runge-Kutta-Nyström Methods with Complex Coefficients Fifth Order Runge-Kutta-Nyström Methods with Complex Coefficients

2012-03-15

arxiv.org/abs/1203.3279v1

Mathematics

Numerical Analysis

11 pages, 3 figures. Submitted to SIAM Journal on Scientific Computing

Scientific paper

We present fifth order Runge-Kutta-Nystr\"om methods, where we allow the timestep coefficients to assume complex values. Among the methods with complex timesteps, we focus on the ones with the coefficients that have positive real parts. This property makes them suitable for problems where a negative coefficient is not acceptable. In addition, the leading order terms in the error expansion of these methods are purely imaginary, effectively increasing the order of the methods by one for real variables.

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