Hello readers, in today’s topic, we will discuss the secant method in numerical analysis/techniques, its formula, derivation, advantages, and limitations with example. This is a very important method to find out the root in numerical analysis. Before these, we also discussed about Regula Falsi Method In Numerical Method, if you don’t know Hurry up Now! Previously we also describe briefly about various topics such as BiSection Method In Numerical Techniques, Newton’s Raphson Method, and many more which are really helpful for your better understanding. So without wasting time let’s dive into our topic:
Secant Method in Numerical Analysis/Techniques
This method is quite similar to the Regula-falsi method except for the condition f(x1)f(x2)<0
In numerical analysis, the secant method is a root-finding procedure that uses a succession of roots of secant lines to better approximate the root of a function f.
From the above graph, we found: The slop of AB = Slop of AC
So for the nth term the formula
It is the derivation of the secant Method in numerical analysis.
Example of Secant Method
A real root of the equation x3-5x+1=0 in the interval of (0,1). Perform four iterations of the Secant Method.
Ans:- The given equation f(x)= x3-5x+1
f(0)= 1
f(1)= -3
from this we found
x0=0 and x1=1
f(x0)=1 and f(x1)=-3 from the secant method
Put n = 1
x2=0.25
f(x2)=f(0.25)= -0.234375
Put n = 2
X3=0.18644
f(x3)= 0.07428
Put n = 3
X4= 0.20174
f(x4)= -0.00048
Put n = 4
X5= 0.20081
So this is all about the Secant Method in Numerical Analysis/Techniques. I hope this is helpful to you. In the next upcoming post we will discuss another new topic of java, so wait for this will meet in the next post. Thank you.
