C Program of Regular-Falsi Method

In this article we will see C Program of Regula-Falsi Method i.e. how to solve the algebraic and transcendental equations using Regula-Falsi Method or False position method.

The Regula–Falsi Method is a numerical method used for calculating the roots of a polynomial f(x).   A value x replaces the midpoint in the Bisection Method and serves as the new approximation of a root of f(x).

We will see a C program for finding a real root of the equation x²+x-1=0 by using Regula-falsi (False Position) Method in the interval [0,1] correct upto three decimal places.

C Program of regula-falsi method

/*  Exp.No 2: Regula-Falsi Method (Finding the roots of given Equ.) */
#include<stdio.h>
#include<conio.h>
#include<math.h>

#define f(x)  x*x+x-1
int main()
{
  float x0,x1,x2, y0,y1,y2, e;
  int maxitr,i;

  printf("Enter two initial starting roots \n");
  scanf("%f%f",&x0,&x1);

  printf("Enter maximum iteration \n");
  scanf("%d",&maxitr);

  printf("Enter the tolerance value \n");
  scanf("%f",&e);

  y0 = f(x0);
  y1 = f(x1);
  if (y0*y1 > 0.0)
     printf("Initial roots are unsuitable \n");
  else
      for(i=1;i<=maxitr;i++)
      {
      x2 = (x0*y1-x1*y0)/(y1-y0);
      y2 = f(x2);
      if (fabs(y2) < e)
      {
          printf("\nsolution is converge \n");
          printf("\nRoot of the given equ.is = %9.4f\n",x2);
          maxitr=i;
      }
      else if(y2*y0 < 0)
           {
           x1=x2;
           y1=y2;
           }
           else
           {
           x0 = x2;
           y0 = y2;
           }
      }
      return 0;
}

OUTPUT

 
Enter two initial starting roots
0 1
Enter maximum iteration
10
Enter the tolerance value
0.0001

solution is converge

Root of the given equ.is =    0.6180

You may also practice :-

• Write a C program for finding a real root of the equation x⁶-x⁴-x³-3 = 0 in the interval 1.5 and 1.6 correct up to four decimal places.
• Write a C program for finding a real root of the equation x³-x²-1 = 0  in the interval 1 and 2 correct up to four decimal places.

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