I have a nonlinear equation f(x)=0 to solve in the interval [0,1]. For physical reasons (I am working with mechanics) the variable x cannot exceed 1 and must be greater than 0. To speed up solving time I use a NR solver. I know there is a solution to f(x)=0 with x in the [0,1] interval, and it is unique.
But on the way to convergence the solver sometimes computes intermediate x values that lie outside the allowable interval, and consequently my system fails and returns physically unacceptable values.
I could use a standard bisection method to solve the eq, but I need high accuracy and convergence speed. Does anybody know about any method to solve the eq with a quadratic rate of convergence, that guarantees that the intermediate steps do not lie outside the interval? Thanks