Computer Algebra Recipes

5.1. CHECKING SOLUTIONS 213
a piecewise function, is slightly harder to verify. One approach is to plot the
velocity pro¯le predicted by the series solution at t =0andcompareitwiththe
analytic piecewise form. Adding, say, the ¯rst ¯ve terms in the series solution,
> psi:=add(psi[n],n=1..5);
8 va(
à :=
p ³
¼x
´ μ
¼ct
2¡1) sin sin
a a
¼3 μ μ
2 ¼x 2 ¼ct
2 vasin sin
a
a
+
c
¼3 c
+ 8
va(
27
p μ μ
3 ¼x 3 ¼ct
2+1)sin sin
a
a
¼3 c
+ 8
va(¡
125
p μ μ
5 ¼x 5 ¼ct
2 ¡ 1) sin sin
a
a
¼3 c
and di®erentiating with respect to time, yields the velocity in the transverse
direction (output suppressed here).
> vel:=diff(psi,t);
To plot the transverse velocity at t = 0, some representative values must be
substituted for the parameters. Vectoria chooses v =5,a =2,andc =1.
> t:=0: v:=5: a:=2: c:=1:
To compare the series representation at t = 0 with the given piecewise initial
velocity distribution, the latter is entered,
> V:=piecewise(x