A Probabilistic Interval Division Method for Solving Nonlinear Equations

In this paper a new iterative method is presented for finding the zeros of a non linear equation using the concept of probability. In this method a sub bracket is produced after bracketing the root by dividing the initial interval into a number of subintervals of equal length. In this work, after assigning a probability to each subinterval, sub bracketing is done by not evaluating the functional value at the each end points of every subinterval but at the end points of some subintervals whose number is effectively less than the total number of subintervals. The method is validated by several numerical examples.