How to insert Integral in a NonLinearProblem

General Usage
1

If I want to have an integral inside a Non Linear System of equations how would I do it with ModelingToolkit.jl and NonLinearSolver.jl?

e.x. I have an integral from 0 to 1 of sin(a*x) which equals to 1, how would I solve for a using NonLinearSolve?

My problem is actually more complex (a lot).

2

You can’t do this with ModelingToolkit’s interface right now, you’ll need to directly write the code for NonlinearSolve.jl until this is supported in the symbolic language.

3

Thanks!, is it on the roadmap?

4

Note that you can just implement this as a numeric integral using any quadrature package, and then pass the resulting function to any root-finding package. For example:

using QuadGK, Roots, ForwardDiff
D(f) = x -> ForwardDiff.derivative(f,float(x))
f(a) = quadgk(x -> sin(a*x), 0, 1, atol=1e-11)[1]
find_zero((f, D(f)), 3, Roots.Newton(), xatol=1e-8)

returns \approx 2\pi. (Be sure to specify an absolute tolerance for any quadrature routine, since you will be looking at parameters where the integral is nearly zero.)

5

It is on the roadmap. So do what Steven says for now, and there’s a lot of other random stuff ModelingToolkit is growing into so I won’t guarantee it’s happening soon but the connections between system types is one of the big focuses.