Regula falsi method

1
The false position methodRegula-Falsi Method
2
Regula-Falsi method
Let given f(x) is continuous in the closed
interval a,b. Such that f(a).f(b)lt0
That means there is a root lies between a and b
for given f(x).
Then a,f(a) and b,f(b) are the two points on
the curve yf(x)..
Thus the equation of the chord joining two points
a,f(a), b,f(b) is as follow
This chord will meet the x-axis when y0. That
means for y0 the resulting x is the approximated
value for the our desired root.
3
Continue
Putting y0 in equation-1 and re arranging all
the terms we have
The x in equation 2 is the approximated root. So
we can write it as xr. Then 2 becomes
The process of finding the approximations
continue till the root is obtained for desired
accuracy.
4
Algorithm for Regula-Falsi method
Let f(x) is continuous in the closed interval
a,b for given f(x)0. Such that
f(a).f(b)lt0
Step-1
Find the approximated root xr by using following
relation.
Step-2
Then Stop the process.
Else go to next step.
Stpe-3
The process of finding the approximations
continue till the root is obtained for desired
accuracy.
5
Example
Find the real root of the equation x3-x-10 by
the method of false position
Ans-
Hence the root is lies between 1 and 2. so a1
and b2.
1st approximation-
6
Continue
2nd approximation-
In similar way we can get the improved
approximations as follow
7
Continue
approx a b xr F(xr)
1st 1 2 1.166666667 -0.578703703
2nd 1.166666667 2 1.252983096 -0.285841435
3rd 1.252983096 2 1.293379386 -0.129775242
4th 1.293379386 2 1.311255776 -0.056693466
5th 1.311255776 2 1.318977679 -0.024349416
6th 1.318977679 2 1.322278105 -0.010381431
7th 1.322278105 2 1.323682334 -0.004412291
From 4th to 7th approximations we concluded that
x1.32 be the required approximation root
8
Thank You ALL

• Presented by
• Boina Anil Kumar
• Asst.Prof in Mathematics
• MITS, Rayagada.
• Odisha, India
• E-mail anil.anisrav_at_gmail.com
• Visit at http//www.mits.edu.in/academics.phpfac
  ulty_BSH-tab

9
Thank You ALL