2
$\begingroup$

I am looking at a system of nonlinear simultaneous equations. The two variables are u>0 and b>0. How can I solve this problem with computer packages, such as Matlab, Python, or Fortran? Thanks.

$$\frac{40000-1.1u^{0.91}40000^{0.091}}{200}-b=0$$

$$640\pi\int_{0}^{b}t\left(\frac{40000-200t}{1.1u}\right)^{10}dt-4000000=0$$

1 Answers 1

2

In Maple I get $u = 28838.13433$, $b = 34.9101911$.

eq1:= (40000 - 11/10*u^(91/100)*40000^(91/1000))/200 - b = 0;

eq2:= 640*Pi*int(t*(40000-200*t)^10/(11/10*u)^10,t=0..b) = 4000000;

bsol:= solve(eq1,b);

f:= unapply(subs(b=bsol,lhs(eq2)),u);

Note first that $u$ can't be too big or it will make $b$ negative in the first equation.

umax:=  fsolve(eval(eq1,b=0));

$$ umax := 35605.43658 $$

U:= fsolve(f(u) = 4e6, u = 0 .. umax);

$$ U := 28838.13433 $$

B:= evalf(eval(bsol,u=U));

$$ B := 34.9101911 $$

  • 0
    I succeeded in replicating your code in Maple. Thank you very much.2012-05-03