ac6a360f-ec47-401c-974e-03b6fba15a07 27 Javier Ochoa 4 5 false false 0 0 decimal

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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 1

M x,time,min y,dye concentration, g/gal 30507011014116319132122242925262618278293330360400440182 mat :

N M 217 range 1 el M 217 range 2 el augment :

xx M 515 range 1 el :

yy M 515 range 2 el :

M yy xx N M

M
x,time,min	y,dye concentration, g/gal
3	0
5	0
7	0
11	0
14	1
16	3
19	13
21	22
24	29
25	26
26	18
27	8
29	3
33	0
36	0
40	0
44	0
#
#
#
#
#

Входные данные:

Input data:

подынтегральная функция

integrand

x f xx yy x cinterp :

a 11 :

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 512

ε 3.7952418 108 -^* -

dint dint ε + :

Ответ:

Result:

dint 218.7892439

AUC 218.8 g * min gal / * : 3468.0505 s kg * m 3^/ *

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

x 1133 range :

n x length :

n 23

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