/*This program in C is used to demonstarte bisection method. Bisection method is one of the many root finding methods. In this method we are given a function f(x) and we approximate 2 roots a and b for the function such that f(a).f(b)<0. Then we find another point c=(a+b)/2 if f(c)==0 then root=c; else if f(a).f(c)<0 b=c; if f(b).f(c)<0 a=c; and we repeat these steps for the given number of iterations*/ #include<stdio.h> #include<math.h> double F(double x) { return(pow(x,3)+3*x-5);//This return the value of the function } int main() { printf("This program illustrates the bisection method in C\n"); printf("x^3 + 3*x - 5 = 0\n"); double x0,x1; printf("Enter the first approximation to the root\n"); scanf("%lf",&x0); printf("Enter the second approximation to the root\n"); scanf("%lf",&x1); int iter; printf("Enter the number of iterations you want to perform\n"); scanf("%d",&iter); int ctr=1; double l1=x0; double l2=x1; double r,f1,f2,f3; //We check if the initail approximations are the root or not if(F(l1)==0) r=l1; else if(F(l2)==0) r=l2; else { while(ctr<=iter) {//this is an implementation of the algorithm mentioned above f1=F(l1); r=(l1+l2)/2.0; f2=F(r); f3=F(l2); if(f2==0) { r=f2; break; } printf("The root after %d iteration is %lf\n",ctr,r); if(f1*f2<0) l2=r; else if(f2*f3<0) l1=r; ctr++; } } printf("The approximation to the root is %lf",r); getch(); } /*A sample run of the program was carried out and the results were found as:- This program illustrates the bisection method in C x^3 + 3*x - 5 = 0 Enter the first approximation to the root 1 Enter the second approximation to the root 2 Enter the number of iterations you want to perform 9 The root after 1 iteration is 1.500000 The root after 2 iteration is 1.250000 The root after 3 iteration is 1.125000 The root after 4 iteration is 1.187500 The root after 5 iteration is 1.156250 The root after 6 iteration is 1.146025 The root after 7 iteration is 1.148438 The root after 8 iteration is 1.152344 The root after 9 iteration is 1.154297 The root is 1.154297 */ |