Adaptive Optimal 𝑚-Stage Runge-Kutta Methods for Solving Reaction-Diffusion-Chemotaxis Systems

Table 3

Comparison for number of iterations among the optimal four-stage RK, RKF 45, and standard four-stage RK. The optimal four-stage RK method is counted four times for the function evaluation per iteration while the RKF 45 is six times per iteration.

Method/Time	1	2	3	4	5
Optimal four-stage RK	816	1832	3052	4472	6096
RKF 45	3480	5598	7152	8910	10866
Std four-stage RK (Δ𝑡=0.004)	1000	2000	Div	Div	Div