Solve nonlinear system equation with integral statement within the nonlinear system

Dear Community

I have a problem which can be described two system equation, with two unknown, the issue here is, inside the equation have complicated integral statement.

F(1) = integration(a(1)*f1(x)+a(2)*f2(x)+integration(a+acosh(a(1)*f3(x)));

F(2) = integration(a(1)*f3(x)+a(2)*f2(x)+integration(a+acosh(a(1)*f1(x)));

above statements are just description only, f1,f2,f3 are just function of x, and the integrations are finite integration from 0 to 1. I have to solve for a(1) and a(2). I can solve similar problem with 1 unknown case, (1 equations with integration and 1 unknown) but I need to solve more variable

Please help me how solve this problem

Regards

Iswan

Answer 1

[Marc]

You can try setting up the your function in a single function file, adding up F(1) and F(2) to say G and try minimizing G with something like fminsearch which uses an nelder mead simplex algorithm, not requiring jacobians or hessians...

If you have the optimization toolbox, there are a bunch of other functions in there they may work. Of course if you want to try brute force, fsolve is something you can play with as well