Which Root-Finding Method Should I Use for an Oscillatory Function?

[a.mlw.walker]

Hi so I have attached a graph, and I am trying to find the first root of the function. I began using Newton Raphson however due to the oscillatory nature of the curve, sometimes NR would not find the first route but an nth route. I need the first. Therefore what I did was compute the first time the function is known to be negative. At this point the x value and the function value are known. It is also known that x = 0 is greater than 1.
My question then is should I use the bisection method as it is guaranteed to solve for a root lying between x = 0 and f(xn) < 0. However it is slow. The secant method requires two initial values so would that work? Or can I use the Newton Raphson method and set a boundary that it knows the route must be before?

Thanks

 

[hotvette]

If you know the interval that contains the root you are looking for, Brent's Method might be a good choice, or a combination of Brent's method (or bisection) to get close, then NR for rapid convergence.

http://en.wikipedia.org/wiki/Brent's_method