Run-times computed for case 1: “Flat”, and normalised to the Wagoner’s method calculation with S_scale = 1000 and y_t,min = 10^-12 (see text). Points indicated with a cross represent calculations that completed successfully with abundances that meet the accuracy criteria outlined in the text. Missing data points represent runs that did not successfully run, either arising from convergence problems within the code or from exceeding the maximum number of time-steps allowed. The labels “W”, “B”, and “G” represent run-times for Wagoner’s, the Bader-Deuflehard, and Gear’s methods, respectively.