Wave Propagation in Linear Media | re-examined

7.5 Test of the quadrature routine
Out[27]= -15
-8.471 10
The next test functions were taken from Sidi [128].
Example 7.5.10
Z 1
0
sin x
x
sinh x
10
sinh 2x dx = arctan tan
10
1
4
tanh 10
4
In[28]:= f[x_] := Sin[x]/x Sinh[1/10 x]/Sinh[2/10 x];
OscInt[f,#&,0] - N[ArcTan[Tan[1/4 Pi] Tanh[10 Pi/4]]]
Out[28]= -13
-2.72449 10
Increasing both WorkingPrecision and NSumExtraTerms,we obtain a result with more correct digits.
Although Sidi gives the exact value of the integral as 0.785398012695720765, the last two digits di er
in the result found by Mathematica as well as in the numerical evaluation of the analytical solution.
In[29]:= OscInt[f,#&,0,WorkingPrecision->34,NSumExtraTerms->30]
Out[29]= 0.78539801269572077061037
In[30]:= N[ArcTan[Tan[1/4 Pi] Tanh[10 Pi/4]],20]
Out[30]= 0.78539801269572077061
Example 7.5.11
Z 1
In[31]:= f[x_] := Sin[Pi/2 x^2];
OscInt[f,Pi/2 #^2&,0] - 0.5
Out[31]= -14
-2.08167 10
0
sin x2
2
185
dx = 1
2