It is not clear to me that your initial guesses are even bracketing your desired tof. So there will be no hope that your bisection method will converge. E.g.,
>> a = (low+high)/2
a =
5.0000e+10
>> f(a)
ans =
875.1905
>> f(high)
ans =
875.1905
>> tof
tof =
1.1257e+03
Also, your function f appears to be monotonically decreasing, not increasing, so your high & low are reversed. E.g., making a couple of changes I can get convergence:
mu = 3.986004418e5;
a = 5000;
c = 9.674486239589160e+03;
s = 1.167624311979458e+04;
tof = 1.1257e+03;
f = @(x) ((x^(3/2))/sqrt(mu))*((2*asin(sqrt(s/(2*x))))-...
(2*asin(sqrt((s-c)/(2*x))))-(sin(2*asin(sqrt(s/(2*x))))-...
sin(2*asin(sqrt((s-c)/(2*x))))));
low = 7500;
high = 20000;
if( (f(low)-tof)*(f(high)-tof) > 0 )
error('Initial guesses do not bracket desired tof');
end
del_t = 0;
while abs(del_t-tof) > 1e-3
a = (low+high)/2;
fa = f(a);
if( imag(fa) )
disp(a);
disp(fa);
error('f(a) is complex');
end
if fa < tof
high = a;
else
low = a;
end
del_t = fa;
end
(But, again, I would advise that you annotate all of your lines with constants on them like I have annotated the first line)
