محاسبات عددی

[pleasehelpme]

یه سری برنامه ی محاسبات عددی:

روش دو بخشی:

//Bisection method
#include<iostream.h>
#include<math.h>
#include<conio.h>
double f(double x){return 3*x-exp(-x);}
void main(){
    float a,b,eps,x;
    int n=1;
    clrscr();
    cout<<"enter a,b,eps:";
    cin>>a>>b>>eps;
    x=(a+b)/2;
    while(fabs(f(x))>=eps){
	  if (f(x)*f(a)>0)
	      a=x;
	  else
	      b=x;
	  x=(a+b)/2;
	  n++;
    }
    cout<<"ROOT = "<<x;
    cout<<"\nITERATION = "<<n;
    getch();
}

نابجایی:

//Regula falsi method
#include<iostream.h>
#include<math.h>
#include<conio.h>
double f(double x) { return x * x * x * x - sinh(x);}
void main(){
     clrscr();
     double eps,a,b,x;
     int n=1;
     cout<<"Enter a,b,eps:";
     cin>>a>>b>>eps;
     x = ( a * f(b) - b * f(a) ) / ( f(b) - f(a) );
     while ( fabs( f(x) ) >= eps ){
	   cout<< x << "\n";
	   if ( f(x)*f(a)>0)
	       a=x;
	   else
	       b=x;
	   x=(a*f(b)-b*f(a)) / (f(b)-f(a));
	   n++;
     }
     cout<<"ROOT = " << x;
     cout<<"\nITERATION = " << n;
     getch();
}

نیوتن:

//Newton-Raphson method
#include<iostream.h>
#include<math.h>
#include<conio.h>
double f( double x ) { return 100 * sin(x) - x;}
double fprime( double x ) { return 100 * cos(x) - 1;}
void main(){
     clrscr();
     double eps,x0,x;
     int n=1;
     cout<< "Enter x0,eps:";
     cin>> x0 >> eps;
     x = x0 - f(x0) / fprime(x0);
     while ( fabs(f(x) ) >= eps){
	   cout<< x << "\n";
	   x0 = x;
	   x = x0 - f(x0) / fprime(x0);
	   n++;
     }
     cout<< "ROOT = "<< x;
     cout<< "\nITERATION = "<< n;
     getch();
}

تکرار ساده:

//Fixed point iteration method
#include<iostream.h>
#include<math.h>
#include<conio.h>
double f(double x){return 100*sin(x)-x;}
double g(double x){return asin(0.01*x);}
void main(){
     clrscr();
     double eps,x0,x1,x;
     int n=1;
     cout<<"Enter x0,eps:";
     cin>>x0>>eps;
     x=g(x0);
     while (fabs(x-x0) >= eps){
	   x0=x;
	   x=g(x0);
	   n++;
     }
     cout<<"ROOt ="<<x;
     cout<<"\nITERATION ="<<n;
     getch();
}

وتری:

/secant method
#include<iostream.h>
#include<math.h>
#include<conio.h>
double f( double x ) {return x * x * x * x - sinh(x);}
void main(){
     clrscr();
     double eps,x0,x1,x;
     int n=1;
     cout<<"Enter x0,x1,eps :\n";
     cin>>x0>>x1>>eps;
     x = x1 - ( f(x1) * (x1-x0) ) / ( f(x1) - f(x0) );
     while( fabs(x1-x0) >= eps ){
	cout<< x0 << "\t" << x1 << "\t" << x << "\n";
	x0 = x1;
	x1 = x;
	x = x1 - ( f(x1) * ( x1 - x0 )) / ( f(x1) - f(x0) );
	n++;
     }
     cout<<"ROOT = " << x;
     cout<<"\nITERATION = " << n;
     getch();
}