-
Notifications
You must be signed in to change notification settings - Fork 21
/
Lobatto.m
executable file
·137 lines (125 loc) · 3.09 KB
/
Lobatto.m
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
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
function [xIP,weight] = Lobatto (nIP)
% locations (xIP) and weights (weight) for nIP integration points
xIP = zeros(nIP,1);
weight = zeros(nIP,1);
switch nIP
case 2
xIP (1) = -1.;
weight(1) = 1.;
xIP (2) = 1.;
weight(2) = 1.;
case 3
xIP (1) = -1.;
weight(1) = 1/3;
xIP (2) = 0.;
weight(2) = 4/3;
xIP (3) = 1.;
weight(3) = 1/3;
case 4
xIP (1) = -1.;
weight(1) = 1/6;
xIP (2) = -0.44721360;
weight(2) = 5/6;
xIP (3) = 0.44721360;
weight(3) = 5/6;
xIP (4) = 1.;
weight(4) = 1/6;
case 5
xIP(1) = -1.;
weight(1) = 0.1;
xIP(2) = -0.65465367;
weight(2) = 0.5444444444;
xIP(3) = 0.;
weight(3) = 0.7111111111;
xIP(4) = 0.65465367;
weight(4) = 0.5444444444;
xIP(5) = 1.;
weight(5) = 0.1;
case 6
xIP(1) = -1.;
weight(1) = 0.06666666667;
xIP(2) = -0.7650553239;
weight(2) = 0.3784749562;
xIP(3) = -0.2852315164;
weight(3) = 0.5548583770;
xIP(4) = -xIP(3);
weight(4) = weight(3);
xIP(5) = -xIP(2);
weight(5) = weight(2);
xIP(6) = -xIP(1);
weight(6) = weight(1);
case 7
xIP (1) = -1.;
weight(1) = 0.04761904762;
xIP (2) = -0.8302238962;
weight(2) = 0.2768260473;
xIP (3) = -0.4688487934;
weight(3) = 0.4317453812;
xIP (4) = 0.;
weight(4) = 0.4876190476;
xIP (5) = -xIP(3);
weight(5) = weight(3);
xIP (6) = -xIP(2);
weight(6) = weight(2);
xIP (7) = -xIP(1);
weight(7) = weight(1);
case 8
xIP(1) = -1.;
weight(1) = 0.03571428571;
xIP(2) = -0.8717401485;
weight(2) = 0.2107042271;
xIP(3) = -0.5917001814;
weight(3) = 0.3411226924;
xIP(4) = -0.2092992179;
weight(4) = 0.4124587946;
xIP(5) = -xIP(4);
weight(5) = weight(4);
xIP(6) = -xIP(3);
weight(6) = weight(3);
xIP(7) = -xIP(2);
weight(7) = weight(2);
xIP(8) = -xIP(1);
weight(8) = weight(1);
case 9
xIP (1) = -1.;
weight(1) = 0.02777777778;
xIP (2) = -0.8997579954;
weight(2) = 0.1654953615;
xIP (3) = -0.6771862795;
weight(3) = 0.2745387125;
xIP (4) = -0.3631174638;
weight(4) = 0.3464285109;
xIP (5) = 0.;
weight(5) = 0.3715192743;
xIP (6) = -xIP (4);
weight(6) = weight(4);
xIP (7) = -xIP (3);
weight(7) = weight(3);
xIP (8) = -xIP (2);
weight(8) = weight(2);
xIP (9) = -xIP (1);
weight(9) = weight(1);
case 10
xIP (1) = -1.;
weight(1) = 0.02222222222;
xIP (2) = -0.9195339082;
weight(2) = 0.1333059908;
xIP (3) = -0.7387738651;
weight(3) = 0.2248893421;
xIP (4) = -0.4779249498;
weight(4) = 0.2920426836;
xIP (5) = -0.1652789577;
weight(5) = 0.3275397611;
xIP (6) = -xIP (5);
weight(6) = weight(5);
xIP (7) = -xIP (4);
weight(7) = weight(4);
xIP (8) = -xIP (3);
weight(8) = weight(3);
xIP (9) = -xIP (2);
weight(9) = weight(2);
xIP (10) = -xIP (1);
weight(10)= weight(1);
otherwise
error('Invalid order for Lobatto integration.')
end