Fifth Order Runge-Kutta-Nystr\"om Methods with Complex Coefficients
  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.
