Wave Propagation in Linear Media | re-examined

7.5 Test of the quadrature routine
Example 7.5.3
Z 1
In[20]:= f[x_] := Sin[x]/Sqrt[1+x];
SetPrecision[OscInt[f,#&,0],16]
Out[20]= 0.8095254817472858
Example 7.5.4
0
Z 1
1
sin x
p 1+x dx =0:809525481747
sin(x + 1
x )
p dx =0:232948197094
x
In[21]:= f[x_] := Sin[x+1/x]/Sqrt[x];
SetPrecision[OscInt[f,(#+1/#)&,1],16]
Out[21]= 0.23294819709403225
Example 7.5.5
Z 1
1
sin(x + 1 p ) x
p dx =0:0416328516893
x
In[22]:= f[x_] := Sin[x+1/Sqrt[x]]/Sqrt[x];
SetPrecision[OscInt[f,(#+1/Sqrt[#])&,1],16]
Out[22]= 0.04163285168937769
In the last two examples it would have also been possible to use only the linear part of the
argument function for the determination of the partition points by substituting the pure
function #& for the respective arguments in the function call. The results would in fact have
been the same.
Some other functions with linearly growing numbers of oscillations have been examined by
Hasegawa and Torii [127].
Example 7.5.6
Z 1
0
e ,x cos xdx = 1
2
183