Page 196 - Numerical Methods for Chemical Engineering

Accuracy and stability of single-step methods 185

1

ct A
A
B
cncentratin 1 2
c 1
1

2
1

2 1
tie t
Figure 4.8 Dynamic concentration profiles for an activated reaction mechanism in the nonstiff
∗
∗
case, k 2 = 1(A + M → A + M, A → B).

1
A
1 1 A
B
ct 1 2
atin 1
cncentr 1

1 c 1 2 1
1

1

1
2 1
tie t

Figure 4.9 Dynamic concentration profiles for the activated reaction mechanism in the stiff case, k 2 =
∗
∗
100 (A + M → A + M, A → B).
Accuracy and stability of single-step methods

Above we have demonstrated the use of MATLAB solvers, with little discussion of their
performance. Here, we address these issues for the restricted class of single-step integrators

x [k+1] = x [k] + ( t) (1 − θ) f x [k] + θ f x [k+1] (4.150)