
The model parameters are l ¼0.2 new cells per cell per week and a ¼0.02 per week.
A tumor initially contains one thousand cells.
(c) Compare results from the exact solution and approximate solutions with a step size of
T ¼0.25 week. Plot the approximate and exact solutions on the same graph.
(a) Combining the derivative function
f
A
(i) ¼ f[t
i
, V
A
(i)] ¼ le
at
i
V
A
(i)(6:196)
with the AB-2 integrator of Equation 6.180, that is,
V
A
(i þ 1) ¼ V
A
(i) þ
T
2
[3f
A
(i) f
A
(i 1)]
yields the second-order difference equation
V
A
(i þ 1) ¼ V
A
(i) þ
T
2
[3le
at
i
V
A
(i) le
at
i1
V
A
(i 1)] (6:197)
¼ 1 þ
3
2
lTe
aiT
V
A
(i)
1
2
lTe
a(i1)T
V
A
(i 1), i ¼ 1, 2, 3, ... (6:198)
Repeating