-
Notifications
You must be signed in to change notification settings - Fork 57
/
line_nco_rule.html
252 lines (213 loc) · 6.75 KB
/
line_nco_rule.html
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
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
<html>
<head>
<title>
LINE_NCO_RULE - Newton Cotes Open (NCO) Quadrature Rules for the Interval
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
LINE_NCO_RULE <br> Newton Cotes Open (NCO) Quadrature Rules for the Interval
</h1>
<hr>
<p>
<b>LINE_NCO_RULE</b>
is a MATLAB library which
computes a Newton Cotes Open (NCO) quadrature rule
using equally spaced points
over the interior of a line segment in 1D.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this
web page are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>LINE_NCO_RULE</b> is available in
<a href = "../../c_src/line_nco_rule/line_nco_rule.html">a C version</a> and
<a href = "../../cpp_src/line_nco_rule/line_nco_rule.html">a C++ version</a> and
<a href = "../../f77_src/line_nco_rule/line_nco_rule.html">a FORTRAN77 version</a> and
<a href = "../../f_src/line_nco_rule/line_nco_rule.html">a FORTRAN90 version</a> and
<a href = "../../m_src/line_nco_rule/line_nco_rule.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/ccn_rule/ccn_rule.html">
CCN_RULE</a>,
a MATLAB program which
defines a nested Clenshaw Curtis quadrature rule.
</p>
<p>
<a href = "../../m_src/chebyshev1_rule/chebyshev1_rule.html">
CHEBYSHEV1_RULE</a>,
a MATLAB program which
computes and prints a Gauss-Chebyshev type 1 quadrature rule.
</p>
<p>
<a href = "../../m_src/chebyshev2_rule/chebyshev2_rule.html">
CHEBYSHEV2_RULE</a>,
a MATLAB program which
computes and prints a Gauss-Chebyshev type 2 quadrature rule.
</p>
<p>
<a href = "../../m_src/clenshaw_curtis_rule/clenshaw_curtis_rule.html">
CLENSHAW_CURTIS_RULE</a>,
a MATLAB program which
defines a Clenshaw Curtis quadrature rule.
</p>
<p>
<a href = "../../m_src/legendre_rule/legendre_rule.html">
LEGENDRE_RULE</a>,
a MATLAB program which
computes a 1D Gauss-Legendre quadrature rule.
</p>
<p>
<a href = "../../m_src/line_felippa_rule/line_felippa_rule.html">
LINE_FELIPPA_RULE</a>,
a MATLAB library which
returns the points and weights of a Felippa quadrature rule
over the interior of a line segment in 1D.
</p>
<p>
<a href = "../../m_src/line_grid/line_grid.html">
LINE_GRID</a>,
a MATLAB library which
computes a grid of points
over the interior of a line segment in 1D.
</p>
<p>
<a href = "../../m_src/line_integrals/line_integrals.html">
LINE_INTEGRALS</a>,
a MATLAB library which
returns the exact value of the integral of any monomial
over the length of the unit line in 1D.
</p>
<p>
<a href = "../../m_src/line_monte_carlo/line_monte_carlo.html">
LINE_MONTE_CARLO</a>,
a MATLAB library which
applies a Monte Carlo method to estimate the integral of a function
over the length of the unit line in 1D;
</p>
<p>
<a href = "../../m_src/line_ncc_rule/line_ncc_rule.html">
LINE_NCC_RULE</a>,
a MATLAB library which
computes a Newton Cotes Closed (NCC) quadrature rule
using equally spaced points
over the interior of a line segment in 1D.
</p>
<p>
<a href = "../../m_src/patterson_rule/patterson_rule.html">
PATTERSON_RULE</a>,
a MATLAB program which
returns the points and weights of a 1D Gauss-Patterson quadrature rule
of order 1, 3, 7, 15, 31, 63, 127, 255 or 511.
</p>
<p>
<a href = "../../m_src/tetrahedron_nco_rule/tetrahedron_nco_rule.html">
TETRAHEDRON_NCO_RULE</a>,
a MATLAB library which
defines Newton-Cotes Open (NCO) quadrature rules
over the interior of a tetrahedron in 3D.
</p>
<p>
<a href = "../../m_src/triangle_fekete_rule/triangle_fekete_rule.html">
TRIANGLE_FEKETE_RULE</a>,
a MATLAB library which
defines Fekete rules for quadrature or interpolation
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../m_src/triangle_felippa_rule/triangle_felippa_rule.html">
TRIANGLE_FELIPPA_RULE</a>,
a MATLAB library which
returns Felippa's quadratures rules for approximating integrals
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../m_src/triangle_nco_rule/triangle_nco_rule.html">
TRIANGLE_NCO_RULE</a>,
a MATLAB library which
defines Newton-Cotes Open (NCO) quadrature rules
over the interior of a triangle in 2D.
</p>
<p>
<a href = "../../m_src/wedge_felippa_rule/wedge_felippa_rule.html">
WEDGE_FELIPPA_RULE</a>,
a MATLAB library which
returns quadratures rules for approximating integrals
over the interior of the unit wedge in 3D.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Philip Davis, Philip Rabinowitz,<br>
Methods of Numerical Integration,<br>
Second Edition,<br>
Dover, 2007,<br>
ISBN: 0486453391,<br>
LC: QA299.3.D28.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "line_nco_rule.m">line_nco_rule.m</a>,
computes a Newton-Cotes Open rule for [A,B] of order N.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>,
prints the YMDHMS date as a timestamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "line_nco_rule_test.m">line_nco_rule_test.m</a>,
a sample calling program.
</li>
<li>
<a href = "line_nco_rule_test_output.txt">line_nco_rule_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "line_nco_rule_test01.m">line_nco_rule_test01.m</a>,
computes and prints some rules.
</li>
<li>
<a href = "line_nco_rule_test02.m">line_nco_rule_test02.m</a>,
uses the rules to integrate a function.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 28 July 2014.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>