       Numerical equation solving

• To: mathgroup at smc.vnet.net
• Subject: [mg116199] Numerical equation solving
• From: florian.maurer at schott.com
• Date: Fri, 4 Feb 2011 06:58:20 -0500 (EST)

```Hi everybody,

I have a quite challenging question about numerical equation solving with
MATHEMATICA:

f1 - f2 + ((f2 - f1) t)/t1 = (r1^2 rho vt^2)/(2 \[Pi] r2^4) (3/2 + l/(2
r2) k/((2 rho vt)/(\[Pi] r2 eta))^(1/4))

The equation given above is implicit when solving to variable vt. The
variable vt itself is a differential operator (D[v,t]), so vt must be
replaced with D[v,t]. As I am interested in v the solution has to be
integrated with respect to t (i.e. Integrate[D[v,t],t,{0,t1}] or Integrate
[D[v,t],t,{0,t1}]). Finally, I want to visualize in a contour plot the
values of f1 and t1 for which the integrated equation fulfills a certain
number q. All variables are positive real numbers.
To maybe better explain my problem I have summarized all steps in one
MATHEMATICA command (I know that the syntax is not correct):

ContourPlot[q = NIntegrate[D[v, t]/.Solve[f1-f2 + ((f2 - f1) t)/t1 ==
(r1^2 rho D[v, t]^2)/(2 \[Pi] r2^4) (3/2 + l/(2 r2) k/((2 rho D[v,
t])/(\[Pi] r2 eta))^(1/4)), D[v, t]],t, {0, t1}], {t1, 0.1, a}, {f1, 0, b}]

How can I solve solve this problem with MATHEMATICA? Thanks in advance for