Nonlinear Equations

Methods for finding roots of equations f(x) = 0. Default function: $f(x) = x^3 - x - 2$

Bisection Method

The bisection method finds a root by repeatedly halving an interval $[a, b]$ where $f(a)$ and $f(b)$ have opposite signs.

c = \frac{a + b}{2}

If $f(a)$ · $f(c)$ < 0, then root is in $[a, c]$ ; otherwise in $[c, b]$ .

Convergence rate: $O(1/2^n)$ — linear convergence

Custom function (press Enter or Apply)

f(x) =

Initial a

Initial b

Tolerance ε