Wave Propagation in Linear Media | re-examined

8 Application of the quadrature routine
Things are di erent with the rectangular wave packet, which is to be treated next. Examining
this case, we see that the di erence at the origin is extremely high. This is no surprise because
at this point wemust not split the integrand like we did in (4.22). The reason is that one of
the resulting integrals does not converge, and this is why we ought to exclude the origin from
the computation (which in fact has been done for the more general driver function Phi).
Example 8.4.5
In[5]:= boundary = Table[ft,PhiInc[x,t,w,k,Shape->Rect]+
PhiRef[x,t,w,k,Shape->Rect]-
(PhiTrans[x,t,w,k,Shape->Rect]+
PhiEvan[x,t,w,k,Shape->Rect])g,ft,0,20g];
ListPlot[boundary/.fx_,y_g:>fx,Abs[y]g,PlotJoined->True,
PlotRange->All];
0.02
0.015
0.01
0.005
5 10 15 20
The best congruence is found for the Gaussian wave, where we have virtually no di erence at
all (this is why Mathematica chooses a wide plot range on the y-axis).
Example 8.4.6
In[6]:= n = 6;
boundary = Table[ft,PhiInc[x,t,w,k,n,Shape->Gauss]+
PhiRef[x,t,w,k,n,Shape->Gauss]-
(PhiTrans[x,t,w,k,n,Shape->Gauss]+
PhiEvan[x,t,w,k,n,Shape->Gauss])g,ft,0,20g];
ListPlot[boundary/.fx_,y_g:>fx,Abs[y]g,PlotJoined->True,
PlotRange->All];
208