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

Table 1

Comparison for number of iterations among optimal two-stage RK, RKF 23, and standard two-stage RK. The optimal two-stage RK method is counted twice for the function evaluation per iteration, while the RKF 23 is counted four times per iteration. “Div” is the abbreviation for Divergent.

Method/Time	1	2	3	4	5
Optimal two-stage RK	638	1278	1918	2558	3200
RKF 23	1175	2765	4310	6075	8250
Std two-stage RK (Δ𝑡=0.0025)	800	1600	2400	Div	Div