Regula Falsi (False Position) Method Algorithm (Step Wise)
False Position Introduction
Regula Falsi (also known as False Position Method) is one of bracketing and convergence guarenteed method for finding real root of non-linear equations.
False Position Method is bracketing method which means it starts with two initial guesses say x0 and x1 such that x0 and x1 brackets the root i.e. f(x0)f(x1)<0
Regula Falsi is based on the fact that if f(x) is real and continuous function, and for two initial guesses x0 and x1 brackets the root such that: f(x0)f(x1) <0 then there exists atleast one root between x0 and x1.
If x0 and x1 are two guesses then we compute new approximated root as:
x2 = x0 - ((x0-x1) * f(x0))/(f(x0) - f(x1))
Now we have following three different cases:
- If f(x2)=0 then the root is x2.
- If f(x0)f(x2)<0 then root lies between x0 and x2.
- If f(x0)f(x2)> 0 then root lies between x1 and x2.
And then process is repeated until we find the root within desired accuracy.
Algorithm for False Position Method
1. start 2. Define function f(x) 3. Choose initial guesses x0 and x1 such that f(x0)f(x1) < 0 4. Choose pre-specified tolerable error e. 5. Calculate new approximated root as: x2 = x0 - ((x0-x1) * f(x0))/(f(x0) - f(x1)) 6. Calculate f(x0)f(x2) a. if f(x0)f(x2) < 0 then x0 = x0 and x1 = x2 b. if f(x0)f(x2) > 0 then x0 = x2 and x1 = x1 c. if f(x0)f(x2) = 0 then goto (8) 7. if |f(x2)|>e then goto (5) otherwise goto (8) 8. Display x2 as root. 9. Stop