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1 function [bp,wf]=ncrule(m) |
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2 %usage: [bp,wf]=ncrule(m); |
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3 % This function returns the Newton-Coates base points and weight factors |
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4 % up to an 8 point Newton-Coates formula. |
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5 % |
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6 % m -- number of Newton-Coates points (integrates an mth order |
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7 % polynomial exactly (or an (m+1)th order for even m)) |
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8 |
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9 % By Bryce Gardner, Purdue University, Spring 1993. |
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10 |
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11 if ( m == 1 ) |
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12 bp=[-1;1]; |
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13 wf=[1;1]; |
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14 elseif ( m == 2 ) |
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15 bp=[-1;0;1]; |
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16 wf=[1;4;1]/3; |
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17 elseif ( m == 3 ) |
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18 bp=[-1;-1/3;1/3;1]; |
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19 wf=[1;3;3;1]/4; |
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20 elseif ( m == 4 ) |
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21 bp=[-1;-1/2;0;1/2;1]; |
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22 wf=[7;32;12;32;7]/45; |
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23 elseif ( m == 5 ) |
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24 bp=[-1;-3/5;-1/5;1/5;3/5;1]; |
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25 wf=[19;75;50;50;75;19]/144; |
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26 elseif ( m == 6 ) |
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27 bp=[-1;-2/3;-1/3;0;1/3;2/3;1]; |
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28 wf=[41;216;27;272;27;216;41]/420; |
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29 elseif ( m == 7 ) |
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30 bp=[-1;-5/7;-3/7;-1/7;1/7;3/7;5/7;1]; |
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31 wf=[751;3577;1323;2989;2989;1323;3577;751]/8640; |
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32 else |
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33 if ( m != 8 ) |
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34 disp('Dont know formula higher than n=8. Returning as if n=8.'); |
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35 endif |
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36 bp=[-1;-3/4;-1/2;-1/4;0;1/4;1/2;3/4;1]; |
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37 wf=[989;5888;-928;10496;-4540;10496;-928;5888;989]/14175; |
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38 endif |
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39 |
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40 endfunction |
