Overview
The regula-falsi method is the oldest method of finding the approximate numerical value of a real root of an equation f(x) = 0.
This method is also known as method of false position. The method used to estimate the roots of a polynomial f(x).
In this method we suppose that x1 and x2 are two points where f(x1) and f(x2) are of opposite sign .Let f(x1) < 0 and f(x2) > 0.
Hence the root of the equation f(x) = 0 lies between x1 and x1 and so, f(x1)f(x2) < 0.
Formula of regula-falsi method
The Regula Falsi formula
Find f(x3) is positive or negative. If f(x3) > 0 then root lies between x3 and x1 or if f(x3) < 0 then root lies between x3 and x1 similarly we calculate x4.
Proceed in this manner until the desired accurate root is found.
Solved example
Example: Apply Regula Falsi Method to solve the equation– 3x – cosx – 1 = 0.
Solution:
let f(x) = 3x – cosx – 1 = 0
by hit and trial
f(0.60) = 0.010351 > 0
So the root of the equation lies between x1=0.60 and x2 = 0.61, also
f(0.60) f(0.61) < 0
By Regula Falsi Mehtod, the first approximation,
now
So, root of the equation f(x) = 0 lies between 0.60709 and 0.61 and also f(0.60709) f(0.61) < 0.
Second approximation
now
So, root of the equation f(x) = 0 lies between 0.60710 and 0.61 and also f(0.60710) f(0.61) < 0.
The third approximation,
Hence the root of the given equation correct to five decimal place is 0.60710.
Interested in learning about similar topics? Here are a few hand-picked blogs for you!