# NUMERICAL METHOD LAB 1 :Bisection Method:

Bisection method is used to find the real roots of a nonlinear equation. The process is based on the ‘Intermediate Value Theorem‘. According to the theorem “If a function f(x)=0 is continuous in an interval (a,b), such that f(a) and f(b) are of opposite nature or opposite signs, then there exists at least one or an odd number of roots between a and b.”

**Features of Bisection Method:**

- Type – closed bracket
- No. of initial guesses – 2
- Convergence – linear
- Rate of convergence – slow but steady
- Accuracy – good
- Programming effort – easy
- Approach – middle point

## Bisection Method Algorithm:

- Start
- Read x1, x2, e

*Here x1 and x2 are initial guesses

e is the absolute error i.e. the desired degree of accuracy* - Compute: f1 = f(x1) and f2 = f(x2)
- If (f1*f2) > 0, then display initial guesses are wrong and goto (11).

Otherwise continue. - x = (x1 + x2)/2
- If ( [ (x1 – x2)/x ] < e ), then display x and goto (11).

* Here [ ] refers to the modulus sign. * - Else, f = f(x)
- If ((f*f1) > 0), then x1 = x and f1 = f.
- Else, x2 = x and f2 = f.
- Goto (5).

*Now the loop continues with new values.* - Stop