I have a nonlinear equation that uses an initial y'(a) and outputs a value y(b) such that y(b)=f(y'(a)), where f(x) is some function. The idea is that I'd like to be able to maximize y(b).
Typically, if I had a value for y(b), I could use the shooting or secant method. However I don't have that value. I was thinking I could use a loop to find the max value, but that is very inefficient. Anything better I could use?
*Edit: Also I do not have an explicit expression for f(x).
Thanks,
Mike