CMEP

Bisection :

#include<bits/stdc++.h>
#define E 0.01
using namespace std;
double functionn(double x){
    return x*x+log(x)-2;
    }
    int n=1;
    double c;
    void bisection(double a , double b){
    if(functionn(a)*functionn(b)>=0)
    {
        cout<<"Incorrect a and b";
        return;
    }
    c=a;
    while((b-a)>=E)
    {
        c=(a+b)/2;
        if(functionn(c)*functionn(a)<0)
        {
          cout<<"Approaximation No"<<n<<" : "<< c<<endl;
          cout<<"functional values"<<c*c+log(c)-2<<endl;
          b=c;}
          else{
            cout<<"Aproaximation No"<<n<<" : " << c<< endl;
            cout<<"functional values="<<c*c+log(c)-2<<endl;
            a=c;
          }
          n++;
          cout<<endl;
    }}

int main(){
    cout<<"Enter input a and b : ";
    double a,b;
    cin>>a>>b;
    cout<<"Here , a="<<a<<" and b="<<b<<endl;
    bisection(a,b);
    cout<<endl;
    cout<<"So the required root is = "<<c<<endl;
    return 0;

}


False Position:

#include<stdio.h>
#include<math.h>
#define t 0.0001
#define F(x) x*x*x-2*x*x-4
int main(){
    float x0,x1,x2,f0,f1,f2;
    printf("Enter the value of x0: ");
    scanf("%f",&x0);
    printf("Enter the value of x1: ");
    scanf("%f",&x1);
    printf("\n_______________________________________________");
    printf("\nx0\t x1\t x2\t f0\t f1\t f2  ");
    printf("\n_______________________________________________");
    do{
        f0=F(x0);
        f1=F(x1);
        x2=x0-((f0*(x1-x0))/(f1-f0));
        f2=F(x2);
        printf("\n%f %f %f %f %f",x0,x1,x2,f1,f2);
        if(F(x0)*F(x2)<0){
            x1=x2;
        }
        else{
            x0=x2;
        }
        }while(fabs(f2)>t||F(x2)==0);
        printf("\n___________________________________________");
        printf("\n\nApproaximation root:%f",x2);

        }



Newton:



#include<stdio.h>
#include<math.h>
#define E 0.0001
#define f(x) sin(x)-1+x*x
#define g(x) cos(x)+2*x
int main(){
    float x0,x1,x2,f0,g0,root;
    int i=1;
    printf("Using Newton Raphson Method to find root of the equation (x*x)-4*x-10\n");
    printf("\n Enter the value of x0 :");

    scanf("%f",&x0);
    printf("Step \t x0\t\t x1\t\t f0\t\tg0\n");
    b:f0=f(x0);
    g0=g(x0);
    x1=x0-(f0/g0);
    printf("%d\t %4f\t %4f\t %4f  \t%4f \n",i,x0,x1,f0,g0);
    i++;
    if(fabs((x1-x0)/x1)<=E){
        root=x1;
        printf("The root is %4f",root);
        goto c;}
        else {
            x0=x1;
            goto b ;
        }
        c:
            getch();
    }




Trapezoid:


#include<stdio.h>
#include<math.h>
#define f(x) x*x*x*x


int main()
{

    int i ,n;
    double a,b,h,x, sum=0, integral;
    printf("Enter hte number of sub-interval :");
    scanf("%d",&n);
    printf("Enter the initial limit : ");
    scanf("%lf",&a);
    printf("Enter the final limit : ");
    scanf("%lf",&b);
    h=fabs(b-a)/n;
    for(i=1;i<n ;i++){
        x=a+i*h;
        sum+=f(x);

    }
    integral=(h/2)*(f(a)+f(b)+2*sum);
    printf("\nThe integral is : %lf \n ",integral);
    return 0;

}