Starting with Bisection Method;
The Bisection Method is a simple and reliable numerical technique for finding a root of an equation f(x) = 0. It works for any continuous function, including both polynomials (e.g., x3 − x − 2 = 0) and transcendental equations (e.g., ex − 3x = 0).
The method is based on the Intermediate Value Theorem, which states that if a continuous function f(x) has values of opposite signs at two points, a and b, then there must be at least one root between them.
Steps In Using Bisection method;
- find two point, say p and q such that p < q and f(p) · f(q) < 0
- find the midpoint of p and q, say t
- t is the root of the given function if f(t) = 0, else follow the next step
- divide the interval [p,q] if f(t) · f(p) < 0, there exist a root between t and p
- else if f(t) · f(q) < 0, there exist a root between t and q
- Repeat above three steps until f(t) = 0.
