If you’re worried about accumulated errors, the best approach is probably to compute first to low precision (.1 or so), and then restart with that as a guess. This will take much less than 2x the time (since the second newton pass will converge very quickly since you start close to the right answer), but should prevent excessive back and forths causing cancellation issues.
Roots.jl do the job. Thanks
Another way is to write the problem like this:
\\ \int_a^x f(x')dx'=K(x)\\
\\ \frac{d}{dx}K(x) = f(x),\quad K(a)=0
Use Differential Equations to solve for K(x) and then use interpolation to find the solution:
NB: I have updated the code above under solution#4
Hi
Suppose you’re to solve for x:
\int_{0}^{x} 5(1-t)^{4} dt=0.9
using Roots, QuadGK
f1(x)=5(1-x)^4
f2(x)=quadgk(f,0,x)[1]-0.9
find_zero(g,0.5)
2 Likes