The Secant Method is similar to Newton’s Method, but, instead of using calculus to find gradients, it calculates gradients (slopes) on a finite basis, that is, taking two points close to one another and estimating the gradient between them.
In this problem let’s replace omega/p with the variable x.
The slope between two points (x₀,f(x₀)) and (x₁,f(x₁)) is:
So the Secant Method to find x₂ is:
A graph shows that there are two positive roots to f(x)=0. We use initial guesses close to these roots to apply the Secant Method.
The tables below show the initial values as x=0.5 and 1.2, and successive iterations using an x increment of 0.1.
More to follow... (see comment)