c91b91e7-4eef-492c-a096-b434624e34cc 11 Javier Ochoa 4 5 false false 0 0 decimal

&[DATE] &[TIME] - &[FILENAME]

Using splines. CE Tutorial. Numerical methods. Chemical Engineering, October 26, 1987. In regions of sharrply different behavior, splines are often superior to polynomials in generating x - y relationships from data. Example 2,

M Time, h Active cell mass, g/L 10203 0.5 3.5 1.5 4 3.0 4.5 5596 11.8 7128 12.5 9 12.5 10 12.5 11 12.5 12 12.5 13 12.4 141215 11.5 16 10.5 17 9.5 18 8.3 19 7.0 20 5.5 21 4.0 22 3.0 23 2.5 262 mat :

N M 225 range 1 el M 225 range 2 el augment :

N M N M

M
Time, h	Active cell mass, g/L
1	0
2	0
3	0.5
3.5	1.5
4	3
4.5	5
5	9
6	11.8
7	12
8	12.5
9	12.5
10	12.5
11	12.5
12	12.5
13	12.4
14	12
15	11.5
16	10.5
17	9.5
18	8.3
19	7
20	5.5
21	4
22	3
23	2.5
#
#
#
#
#

xx M 225 range 1 el :

yy M 225 range 2 el :

Входные данные:

Input data:

подынтегральная функция

integrand

x f xx yy x cinterp :

a 2 :

нижний предел интегрирования

inferior limit

b 33 :

верхний предел интегрирования

superior limit

maxerr 107 -^:

точность вычисления

accuracy

a b h n simp 13 / h 2 / a f b f + (* h a k h * + f k 1 n 1 - sum * + (* 23 / h * a h 2 / - k h * + f k 1 n sum * + :

Расчёт:

Calculation:

n 2 :

h b a - n / :

dintp a b h n simp :

ε dintp :

ε abs maxerr > n 2 n * : h b a - n / : dint a b h n simp : ε dint dintp - 15 / : dintp dint : 51 line while

n 1024

ε 1.7101002 108 -^* -

dint dint ε + :

Ответ:

Result:

dint 104.1007104

AUC 218.8 g * min L / * : 13128 s kg * m 3^/ *

Now we can plot the graph for the experimental data and the interpolated curve with cubic splines.

x 223 range :

n x length :

n 22

j 1 n range y j el xx yy x j el cinterp : for

x y char size color plotG n x length : plot x 1 el y 1 el char size color augment : i 2 n range plot plot x i el y i el char size color augment stack : for plot 41 line :

plot1 xx yy . 10 Dark Blue plotG :

u x y augment :

plot1 u 2 1 sys