Solution of non-linear equations using bisection method by new technical method

Abstract EN

Numerical approximation of the root-finding problem its important tool for process involves finding a root, or solution of nonlinear equation of the form f (x) = 0, for a given function f.

a root of this equation is also called a zero of the function when we implementing the method on a computer we need to consider the effects of round-off error.

for example the computation of the midpoint of the interval ]an, bn[ should be found from the equation .

the bisection method is used to determine to any specified accuracy that your computer will permit a solution to f (x) = 0 on an interval ]a, b[, provided that f is continuous on the interval and that f (a) and f (b) are of opposite sign.

although the method will work for the case when more than one root is contained in the interval ]a, b[, we assume for simplicity of our discussion that the root in this interval is unique.

the method stops if one of the midpoints happens to coincide with the root.

it also stops when the length of the search interval is less than some prescribed tolerance.

the having method is characterized by the fact that it always includes convergence of the individual islands.

it is also characterized by the case of calculating errors, but one of its disadvantages is that it is slow to converge to reach the solution.

to compare with the a new technical method of the solution .

we followed applied numerical method using a new technical method in computer and we found that the new technical method of solution is much faster and more accurate.