Adaptive Time-Stepping Using Control Theory for the Chemical Langevin Equation

Table 1

The stiff model: the number of steps taken by the I-adaptive, PI-adaptive, and fixed step-size methods on the time-interval [0, 2 × 10⁻²].

	Method	Tried steps	Accepted steps	Failed steps	Error/
1	I-adapt.	1943	1357	585	0.9985
	PI-adapt.	1800	1652	148	0.9971
	Fixed	1943	—	—	56.7290
10^−1	I-adapt.	5298	3910	1388	0.9995
	PI-adapt.	4926	4587	339	0.9990
	Fixed	5298	—	—	76.2772
10^−2	I-adapt.	14590	11543	3046	0.9998
	PI-adapt.	13816	13061	755	0.9997
	Fixed	14590	—	—	100.6531