Write a program that implements the bisection method for root finding. Your prog

Question

Write a program that implements the bisection method for root finding. Your program should be similar to the Etter & Ingber Chapter 6_9 program since it is a variation on the same technique. Your program should find the roots to some user defined tolerance. eventually the program should be able to accept a polynomial to find wiens law according to the planck radiation formula. at least i believe it is a polynomial. i will have to post this problem several times to get it finished but any help is appreciated.

/*----------------------------------------------------*/
/* Program chapter6_9 */
/* */
/* This program estimates the real roots of a */
/* polynomial function using incremental search. */
#include<iostream> //Required for cin, cout
#include<cmath> //Required for cell()
using namespace std;
// Function Prototypes
void check_roots(double left, double right, double a0,
double a1, double a2, double a3);
double poly(double x, double a0, double a1,
double a2, double a3);
int main()
{
// Declare objects and function prototypes.
int n;
double a0, a1, a2, a3, a, b, step, left, right;
// Get user input.
cout << "Enter coefficients a0, a1, a2, a3: ";
cin >> a0 >> a1 >> a2 >> a3;
cout << "Enter interval limits a, b (a<b): ";
cin >> a >> b;
cout << "Enter step size: ";
cin >> step;
//Check subintervals for roots.
n = ceil((b - a)/step);
for (int k=0; k<=n-1; k++)
{
left = a + k*step;
if (k == n-1)
{
right = b;
}
else
{
right = left + step;
}
check_roots(left,right,a0,a1,a2,a3);
}
check_roots(b,b,a0,a1,a2,a3);
// Exit program.
return 0;
}/
*----------------------------------------------------*/
/* This function checks a subinterval for a root. */
void check_roots(double left, double right, double a0,
double a1, double a2, double a3)
{
// Declare objects and function prototypes.
double f_left, f_right;
// Evaluate subinterval endpoints and
// test for roots.
f_left = poly(left,a0,a1,a2,a3);
f_right = poly(right,a0,a1,a2,a3);
if (fabs(f_left) < 0.1e-04)
{
    cout << "Root detected at " << left << endl;
}
else
{
    if (fabs(f_right) < 0.1e-04)
      ;
    else
    {
      if (f_left*f_right < 0)
      {
        cout << "Root detected at " << (left+right)/2) << endl;
      }
    }
}
// Exit function.
return;
}
/*----------------------------------------------------*/
/* This function evaluates a cubic polynomial. */
double poly(double x, double a0, double a1, double a2,
double a3)
{
return a0*x*x*x + a1*x*x + a2*x + a3;
}
/*-------------------

Modern Physics: The black body radiation curve has a peak that can be determined by by maximizing the Planck radiation formula in frequency form with respect to frequency The Planck radiation formula is Tu h3c3 hv/kT If we take the derivative of the equation above and set it equal to zero and then substitute x (hv/kT) we get an expression that reduces to Solve for the roots of this equation to determine the constant for Wien's law. Use the bisection method and the Newton Raphson method. You will need to replace the function in each program with equation 1 above From your value of x determine the constant in Wien's law: Constant c TO in Kelvin) Add a few lines of code to each program to (a) calculate the value of the constant and (b) compare your results to the standard constant (i.e. take a error) from a your textbook.

Explanation / Answer

void check_roots(double left, double right, double a0,
double a1, double a2, double a3)
{
// Declare objects and function prototypes.
double f_left, f_right;
// Evaluate subinterval endpoints and
// test for roots.
f_left = poly(left,a0,a1,a2,a3);
f_right = poly(right,a0,a1,a2,a3);
if (fabs(f_left) < 0.1e-04)
{
    cout << "Root detected at " << left << endl;
}
else
{
    if (fabs(f_right) < 0.1e-04)
      ;
    else
    {
      if (f_left*f_right < 0)
      {
        cout << "Root detected at " << (left+right)/2) << endl;
      }
    }
}
// Exit function.
return;
}
/*----------------------------------------------------*/
/* This function evaluates a cubic polynomial. */
double poly(double x, double a0, double a1, double a2,
double a3)
{
return a0*x*x*x + a1*x*x + a2*x + a3;
}

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