Secant Method in Numerical Analysis/Techniques 2022

Secant Method in Numerical Analysis/Techniques 2022

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 critical method to find out the root of numerical analysis. Before these, we also discussed Regula Falsi Method In Numerical Method, if you don’t know Hurry up Now! Previously we also described briefly 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.

graphical representation of secant method
graphical representation of secant method

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.

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