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

Table 2

Comparison for number of iterations among the optimal three-stage RK, RKF 34, and standard three-stage RK. The optimal three-stage RK method is counted three times for the function evaluation per iteration, while the RKF 34 is five times per iteration.

Method/Time	1	2	3	4	5
Optimal three-stage RK	678	1524	2535	3717	5067
RKF 34	3925	6325	7935	9655	11570
Std three-stage RK (Δ𝑡=0.003)	1002	2001	3000	Div	Div