ABSTRACT
The solution of many scientific and engineering problems requires finding the roots of equations that can be nonlinear. In general, requires a large number of calculations, particularly if the roots are to be determined to a high degree of precision. The bisection method is an extension of the direct-search method for cases when it is known that only one root occurs within a given interval of x. Since numerical methods for finding the roots of functions are iterative, it is important to include a convergence criterion into the process of finding a root; otherwise, a computerized solution could continue to iterate indefinitely. Although the bisection method will always converge on the root, the rate of convergence is very slow. A faster method for converging on a single root of a function is the Newton–Raphson iteration method. The Newton–Raphson iteration usually converges to a root faster than does the bisection method.
