.png)
In this article, we will be going to study the Secant method in numerical analysis and design using Python.
Algorithm
Read a,b,E
Compute f(a) and f(b)
for i=1 to n in steps of 1 do
m=af(b)-bf(a)/f(b)-f(a)
if(|f(m)|<E) then
a=b and b=m
endif
else
Write does not converge a,b,f(a),f(b)
endfor
Write convergent solution m,f(m)
stop
Flowchart
Program
import math
def f(x):
return x*x*x - x -1
def secant(a,b):
if (f(a) * f(b) <0.0):
while True:
m=(a*f(b)-b*f(a))/(f(b)-f(a))
a=b
b=m
if (abs(f(m)) < 0.0001):
break
print("Root",round(m,4))
else:
print("Cannot find roots")
a =1.0
b = 2.0
secant(a, b)
Example
Q]Find the real root of the equation x^3-x-1=0 by secant method up to 4 decimal places?
Solution-
F(x)=x^3-x-1
To find x0 and x1
F(0)=-1 , F(1)=-1 , F(2)= 5
Root[1,2]
F(1.5)=0.875 , F(1.4)=0.343 , F(1.3)= -0.103
Changing x0= 1.3 and x1= 1.4
F(x0)= -0.103 and F(x1)= 1.323042
(First case) x2=x0*F(x1)-x1*F(x0) =1.323042
F(x1)-F(x0)
F(x2)= -0.007136
(Second case) x3=x1*F(x2)-x2*F(x1) =1.323605
F(x2)-F(x1)
F(x2)= -0.000481
(Third case) x4=x2*F(x3)-x3*F(x2) =1.324717
F(x3)-F(x2)
F(x2)= -0.000004
Hence the correct answer(root) up to 4 decimal places is x=1.3247
Happy Coding!
Follow us on Instagram @programmersdoor
Join us on Telegram @programmersdoor
Please write comments if you find any bug in the above code, or want some updates.
Follow Programmers Door for more.
Comments