Regular Falsi Method:-
Definition:-
In Numarical Analysis, for finding root of Algebraic and transcendental equation, we are use Regular Falsi Method.
Working Rules:-
1:- Given equation is f(x) =0 .
Find x₀ and x₁ such that f(x₀) < 0 , f(x₁) > 0 .
∴Root lies between x₀ and x₁ .
2:- We find two point ( x₀ , f(x₀) ) and (x₁ , f(x₁) ), in f(x) curve.
Then we join ( x₀ , f(x₀) ) and (x₁ , f(x₁) ) point by a stragitht line.
We input y = 0 to find a point which point cross x axis.
Let at x₂ ,cross x asis the stragith line.
Now , X₂ = [x₀ . f(x₁) - x₁ f(x₂) ] / [ f(x₁) - f(x₀) ]
Now we examine f(x₂) and its sign.
3:- If f(x₂) = 0 ,So x₂ is the root of the equation.
If f(x₂) > 0, root lies between x₂ and x₀.
Then process to like 2nd step.
If f(x₂) < 0, root lies between x₂ and x₁.
Then process ti like 2nd step.
Example of Regular Falsi Method:-
Question 1:-
Find the real root of the equation x³ + 7x + 9 =0 upto 2 decimal place.
Sloution:-
The given equation is f(x)= x³ + 7x + 9 =0
Now, we are find x₀ and x₁ such that f(x₀)< 0 and f(x₁) > 0
f(0) = 0+ 0+ 9 = 9 > 0
f( -1) = 1 - 7 + 9 = 3 > 0
f( -2)= -8 -14 +9 = -13 < 0
Root lies on (-1) to (-2)
f(-1.5)= -4.875 < 0
f(-1.4) = -3.544<0
f(-1.1)= -0.037< 0
f(-1.09) = 0.074971 >0
Let x₀= -1.1 and x₁ = -1.09
By Regular Falsi Method new aproximate root x₂ = [x₀ . f(x₁) - x₁ f(x₀) ] / [ f(x₁) - f(x₀) ]
= [-1.09(-0.037) + 1.1(0.074971)] / [-0.037 - 0.074971]
= [0.1227981] / [-0.111971]
= -1.09669557
Now f(-1.09669557)= 0.004090 (Correct uptp 2 decimalplace)
Root of the givrn equation is -1.09669557
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