Write a program that solves a nonlinear equation f(x) = 0 using one of closed domain methodsthat we discussed in class (bisectional, false position). Your code can be written from scratch,

Answered: Write a program that solves a nonlinear…

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Solution:

Note: A Java program for nonlinear f(x)=0 using bisectional closed domain method.

considering the f(x)=x²-3 Therefore the equation we consider is x²-3=0 for the interval {0...4}

Program Approach:

create a class
Define main method
initialize arbitrary variable epsilon as static double final double epsilon = 0.00001;
double a, b, m, y_m, y_a
initialize interval a,b as 0,4 and declare the variable m as the midpoint as double.
a = 0; b = 4;
Using While condition find the midpoint and perform the Bisection method as follows:

Bisectional method:

The Bisection Method contains an initial interval [a..b] that has a root
(To find the initial interval we use the property f(a) ≠ sign of f(b))
In this Method we will divide the interval into 2 halves and check that which half interval has a root of the function.
In this Method we will divide the interval into 2 halves and check that which half interval has a root of the function
The the interval is divided in halves till interval is extremely small.
The root will be approximately equal to the obtained final interval.
Finally the Approximate solution contains the roots value.