Now the root lies between a and x1 or x1 and b accordingly if f(a) and f(x1) have an opposite sign or f(b) and f(x1) have opposite signs respectively. Then The root lies between a and b and the first approximation of the root is x1=(a+b)/2. If a function f(x) is continuous in a closed interval and f(a) and f(b) have opposite sign. This method is actually using Intermediate Value Property repeatedly. However, it is the simplest method and it never fails.Īlso Read: Regula Falsi Method C++ Bisection Method Rule You can find more Numerical methods tutorial using MATLAB here.The convergence in the bisection method is linear which is slow as compared to the other Iterative methods.

If you have any questions regarding bisection method or its MATLAB code, bring them up from the comments. But, this root can be further refined by changing the tolerable error and hence the number of iteration. It is slightly different from the one obtained using MATLAB program. The table shows the entire iteration procedure of bisection method and its MATLAB program: The process is then repeated for the new interval. f(b) * f(c) > 0 : if the product of f(b) and f(c) is positive, the root lies in the interval.f(c) = 0 : c is the required root of the equation.The function is evaluated at ‘c’, which means f(c) is calculated. If c be the mid-point of the interval, it can be defined as:

The first step in iteration is to calculate the mid-point of the interval. Here’s how the iteration procedure is carried out in bisection method (and the MATLAB program): The intermediate value theorem can be presented graphically as follows: According to the theorem: “If there exists a continuous function f(x) in the interval and c is any number between f(a) and f(b), then there exists at least one number x in that interval such that f(x) = c.” Bisection Method Theory:īisection method is based on Intermediate Value Theorem. Here, we’re going to write a source code for Bisection method in MATLAB, with program output and a numerical example. Compared to other rooting finding methods, bisection method is considered to be relatively slow because of its slow and steady rate of convergence.Įarlier we discussed a C program and algorithm/flowchart of bisection method. The convergence is linear and it gives good accuracy overall. This method is closed bracket type, requiring two initial guesses. This method is applicable to find the root of any polynomial equation f(x) = 0, provided that the roots lie within the interval and f(x) is continuous in the interval. Bisection method is a popular root finding method of mathematics and numerical methods.

C program for bisection method