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73 lines
2.3 KiB
C++
73 lines
2.3 KiB
C++
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/*----------- NEWTON RAPHSON METHOD TO FIND ROOT OF AN EQUATION -------*/
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/* THE EXPRESSION FOR AN EQUATION IS DEFINED IN function fx
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YOU CAN WRITE DIFFERENT EQUATION IN function fx.
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HERE,
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f(x) = x*x*x - 5*x + 3
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INPUTS : 1) Initial approximation x0 to the root.
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2) Number of iterations.
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OUTPUTS : Value of the root. */
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/*------------------------------ PROGRAM ----------------------------*/
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#include<stdio.h>
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#include<math.h>
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#include<stdlib.h>
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#include<conio.h>
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void main()
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{
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double fx ( double x); /* DECLARATION OF FUNCTION */
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double f_x ( double x); /* CALCULATION OF DERIVATIVE */
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double x0,x1,f_0,f0;
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int n,i;
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clrscr();
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printf("\n NEWTON RAPHSON METHOD TO FIND ROOT OF AN EQUATION");
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printf("\n\n f(x) = x*x*x - 5*x + 3");
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printf("\n\nEnter the value of initial "
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"approximation x0 = ");
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scanf("%lf",&x0);
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/* INITIAL APPROXIMATION x0 IS TO BE ENTERED HERE */
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printf("\nEnter the number of iterations = ");
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scanf("%d",&n);
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printf("\npress any key for display of iterations...\n");
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getch();
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i = 0;
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while(n-- > 0)
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{
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f0 = fx(x0); /* CALCULATE f(x) AT x = x0 */
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f_0 = f_x(x0); /* CALCULATE f'(x) AT x = x1 */
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x1 = x0 - (f0/f_0);
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/* CALCULATION OF NEXT APPROXIMATION */
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i++;
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printf("\n%d x%d = %lf \n"
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"\n f%d = %lf f_%d = %lf x%d = %lf\n"
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,i,i-1,x0,i-1,f0,i-1,f_0,i,x1);
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x0 = x1;
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getch();
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}
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printf("\n\nThe value of root is = %20.15lf",x1); /* ROOT */
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}
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/*---------- FUNCTION PROCEDURE TO CALCULATE VALUE OF EQUATION --------*/
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double fx ( double x)
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{
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double f;
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f = x*x*x - 5*x + 3; /* FUNCTION f(x) */
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return(f);
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}
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/*---------- FUNCTION PROCEDURE TO CALCULATE f'(x0) --------------------*/
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double f_x ( double x)
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{
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double f_dash;
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f_dash = 3*x*x - 5; /* DERIVATIVE OF f(x) i.e. f'(x) */
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return(f_dash);
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}
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/*--------------------- End of program --------------------------------*/
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