blob: d098739f6e28c51ebaf97d898f5e7853e850ea49 (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
|
//Eg-14.2
//pg-582
clear
clc
close()
//Approximate the first and second derivatives using central difference formula
//At i = 1 ; 14y0 - 37y1 + 18y2 = 0;
// Using y0 = 0
// -37y1 + 18y2 = 0 (1)
//At i = 2 ; 14y1 - 37y2 + 18y3 = 0; (2)
//At i = 3 ; and taking y4 = 1 ; 14y2 - 37y3 = -18; (3)
//We have 3 equations and 3 unknowns
A = [-37 18 0;14 -37 18;0 14 -37];
B = [0;0;-18];
//Thomas method
b0 = -37;
c0 = 18;
a1 = 14;
b1 = -37;
c1 = 18;
a2 = 14;
b2 = -37;
r0 = 0;
r1 = 0;
r2 = -18;
B0 = b0;
G0 = r0/B0;
B1 = b1 - a1*c0/B0;
G1 = (r1 - a1*r0)/B1;
B2 = b2 - a2*c1/B1;
G2 = (r2 - a2*r1)/B2;
x(3) = G2;
x(2) = G1 - c1*x(3)/B1;
x(1) = G0 - c0*x(2)/B0;
disp(x)
y(1) = 0; //BC 1
y(2:4) = x(1:3);
y(5) = 1 //BC 2
x1 = 0:0.25:1;
plot(x1,y,'ks')
xlabel('x')
ylabel('y')
|
