This code reproduces the figures 3a, 3b, 4a, 4b, 6a, 6b and 7b of the article “Optimal stability polynomials for numerical integration of initial value problems” (David I. Ketcheson and Aron J. Ahmadia, 2012). The user can fix the number of stages (s) and the order p, and then retrieve (1) the scaled size of real axis interval inclusion for optimized methods Hopt/s^2 (Table 1, page 12), (2) the scaled size of imaginary axis inclusion for optimized methods Hopt/s (Table 2, page 13), (3) the relative size of largest disk that can be included in the stability region scaled by the number of stages (Figure 5, page 15) and (4) the optimal effective step size (Figure 7a, page 16). Please note that updated code is available at http://numerics.kaust.edu.sa/RK-opt/

Proceedings in Applied Mathematics and Mechanics (2014)

Himpe Christian and Ohlberger Mario