Question

if f (x)=0,f(a)<0,f(b)>0,then
formula for regula falsi methon​

Answer 1

Answer:

REGULA-FALSI METHOD

The convergce process in the bisection method is very slow. It depends only on the choice of end points of the interval [a,b]. The function f(x) does not have any role in finding the point c (which is just the mid-point of a and b). It is used only to decide the next smaller interval [a,c] or [c,b]. A better approximation to c can be obtained by taking the straight line L joining the points (a,f(a)) and (b,f(b)) intersecting the x-axis. To obtain the value of c we can equate the two expressions of the slope m of the line L.

m = f(b) - f(a) = 0 - f(b)

(b-a) (c-b)

=> (c-b) * (f(b)-f(a)) = -(b-a) * f(b)

c = b - f(b) * (b-a)

f(b) - f(a)

Now the next smaller interval which brackets the root can be obtained by checking

f(a) * f(b) < 0 then b = c

> 0 then a = c

= 0 then c is the root.

Selecting c by the above expression is called Regula-Falsi method or False position method.