Chapter 07.03 Simpson's 1/3 Rule for Integration-More Examples ...
Chapter 07.03 Simpson's 1/3 Rule for Integration-More Examples ...
Chapter 07.03 Simpson's 1/3 Rule for Integration-More Examples ...
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<strong>07.03</strong>.4 <strong>Chapter</strong> 07.02<br />
z4<br />
<br />
f z n<br />
<br />
f <br />
f<br />
0.6560<br />
2<br />
0.6560<br />
f (0.6560) e<br />
0.65029<br />
<br />
<br />
n1<br />
n2<br />
b a<br />
erfc0<br />
.6560<br />
f z<br />
<br />
<br />
<br />
<br />
0<br />
4<br />
f zi<br />
2 f zi<br />
f zn<br />
3n<br />
<br />
i1<br />
i2<br />
<br />
iodd<br />
ieven<br />
<br />
<br />
<br />
3<br />
2<br />
0.6560 5<br />
f 5 4 <br />
<br />
<br />
f zi<br />
2 f zi<br />
f 0.6560<br />
3 4<br />
<br />
i1<br />
i2<br />
<br />
iodd<br />
ieven<br />
<br />
4.3440<br />
f<br />
5 4 f z1 <br />
4 f z3<br />
<br />
2 f z2<br />
<br />
f 0.6560<br />
12<br />
4.3440 f 5 4 f 3.9140<br />
4 f 1.7420<br />
<br />
12<br />
<br />
<br />
<br />
<br />
2 f 2.8280 f 0.6560 <br />
11<br />
7<br />
4.3440 1.388810<br />
42.222610<br />
<br />
40.048096<br />
<br />
<br />
4<br />
12<br />
<br />
2 3.3627 10<br />
0.65029<br />
<br />
0.30529<br />
b) The exact value of the above integral cannot be found. For calculating the true error and<br />
relative true error, we assume the value obtained by adaptive numerical integration using<br />
Maple as the exact value.<br />
0.6560<br />
.6560<br />
e<br />
<br />
z<br />
erfc 0 dz<br />
0.31333<br />
so the true error is<br />
True Value Approximate Value<br />
E t<br />
5<br />
<br />
0.31333<br />
0.30529<br />
0.0080347<br />
c) The absolute relative true error, <br />
t<br />
, would then be<br />
True Error<br />
t<br />
<br />
100<br />
True Value<br />
0.0080347<br />
<br />
100<br />
0.31333<br />
2.5643 %<br />
2
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