Figure 4: Frequency graph for the phosphoric acid test case

Gallic acid test case

The results for the gallic acid test case (Figure 5) confirm those of the phosphoric acid test case. The inner fixed-point algorithm requires the most iterations to converge (approximately 150). The full Newton algorithm usually requires fewer iterations (approximately 130) but sometimes requires many more iterations (200); sometimes it fails to converge at all (0.05 % failure rate, see Table 5). The outer fixed-point algorithm converges with the fewest iterations (77 iterations maximum). Moreover, this algorithm gives the sharpest frequency graph, indicating that it is not sensitive to the initial guess.