Numerical Program

Newton Raphson Method Definition

In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.

Features of Newton Raphson Method:

  • Type – open bracket
  • No. of initial guesses – 1
  • Convergence – quadratic
  • Rate of convergence – faster
  • Accuracy – good
  • Programming effort – easy
  • Approach – Taylor's series

Program of Newton Raphson in C Language

  #include<stdio.h>
  #include<conio.h>
  #include<math.h>
  #define e 0.001
  #define F(x) (2*x)-3
  float frac(float a)
  {
    float f1;
    f1=a*a-3*a+2;
    return f1;
  }

  void main()
  {
    float x1,x2,f1=0,f2,er,d;
    printf("F(x) = x^2-3x+2\n\n");
    printf("Enter the value of x1: ");
    scanf("%f",&x1);
    printf("\nx1 = %f",x1);
    printf("\n______________________________________________________\n");
    printf(" x1 | x2 | f1 | f'1 | |(x2-x1)/x2| | \n");
    printf("--------------------------------------------------------\n");
    do
    {
        f1=frac(x1);
        d=F(x1);
        x2=x1-(f1/d);
        er=fabs((x2-x1)/x2);
        printf(" %f | %f | %f | %f | %f | \n",x1,x2,f1,d,er);
        x1=x2;
    }
    while(er>e);
    printf("-------------------------------------------------------\n\n");
    printf("\n Root of the equation is: %f",x2);
    getch();
    
  }
    

Output

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