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root finder

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Submitted on: 7/16/2012 11:21:42 AM
By: Sophonias Berhanu  
Level: Advanced
User Rating: Unrated
Compatibility: Borland C++
Views: 1531
(About the author)
 
     finds roots to an equation using methods of bisection, false position, secant, iteration and newton's method
 
code:
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  1. You may use this code in your own programs (and may compile it into a program and distribute it in compiled format for languages that allow it) freely and with no charge.
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//**************************************
// Name: root finder
// Description:finds roots to an equation using methods of bisection, false position, secant, iteration and newton's method
// By: Sophonias Berhanu
//
//This code is copyrighted and has// limited warranties.Please see http://www.Planet-Source-Code.com/vb/scripts/ShowCode.asp?txtCodeId=13806&lngWId=3//for details.//**************************************

#include<iostream.h>
#include<conio.h>
#include<math.h>
#include<iomanip.h>
long double funct(long double x)
{
 long double y;
 y=(sin(x)-x+(0.5));
 return y;
 }
 long double functI(long double x) //funct(x)=0 => x=sin(x)+0.5//
{//fixed point iteration method//
 long double y;
 y=(sin(x)+(0.5));
 return y;
 }
 long double functN_D(long double x) //derivative of funct(x)//
{ //newton-rapson method//
 long double y;
 y=(cos(x)-1);
 return y;
 }
 long double newton(long double x0,int m,long double e,long double sigma)
{
 int i;
 long double x1;
 for (i=0;i<m;i++)
 {
	if (fabs(functN_D(x0))>sigma)
	{
	x1=x0-((funct(x0))/(functN_D(x0)));
	cout<<setw(20)<<x0<<setw(20)<<x1<<setw(25)<<setw(25)<<fabs(funct(x1))<<endl;
	x0=x1;
	}
	else if (!(fabs(functN_D(x0))>sigma))
break;
 }
 if ((fabs(funct(x0))<e) && (fabs(functN_D(x0))>sigma))
 cout<<"\n\n\n"<<setw(25)<<x0<<" Is the approxmate root:";
 else if (!(fabs((funct(x0)))<e) && (fabs(functN_D(x0))>sigma))
 cout<<"\n\n\n"<<setw(25)<<"no convergence in "<<m<<" interations.";
 else if (!(fabs(functN_D(x0))>sigma))
 cout<<"\n\n\n"<<setw(25)<<"Division by zero.";
 getch();
 return 0;
}
long double Iteration(long double x,int m,long double e)
 {
	long double y;
	int i;
 for (i=0;i<m;i++)
 {
y=functI(x);
	cout<<setw(20)<<x<<setw(20)<<y<<setw(25)<<setw(25)<<fabs(x-y)<<endl;
x=y;
 }
 if (abs(funct(x))<e)
 cout<<"\n\n\n"<<setw(25)<<x<<" Is the approxmate root:";
 else if(!abs((funct(x)<e)))
 cout<<"\n\n\n"<<setw(35)<<"No convergence in "<<m<<" iterations:";
 getch();
 return 0;
 }
 long double Secant(long double x0,long double x1,int m,long double e)
{
int i;
long double x2;
for (i=0;i<m;i++)
{
 x2=x1-funct(x1)*((x1-x0)/(funct(x1)-funct(x0)));
 cout<<setw(20)<<x0<<setw(20)<<x1<<setw(25)<<setw(25)<<fabs(funct(x2))<<endl;
 x0=x1;
 x1=x2;
}
if(fabs(funct(x2))<e)
cout<<"\n\n\n"<<setw(25)<<x2<<" Is the approxmate root:";
else
cout<<"\n\n\n"<<setw(30)<<"Doesn't converge in "<<m <<" iterations.";
getch();
return 0;
}
long double False_position(long double a,long double b,int m,long double e)
{
 int i;
 long double ans;
 for(i=0;i<m;i++)
 {
 ans=a-funct(a)*(b-a)/(funct(b)-funct(a));
 cout<<setw(20)<<a<<setw(20)<<b<<setw(25)<<setw(25)<<funct(ans)<<endl;
 if((funct(ans)*funct(b))<0)
 a=ans;
 else if ((funct(ans)*funct(a))<0)
 b=ans;
 }
 if (e>fabs(funct(ans)))
 cout<<"\n\n\n"<<setw(25)<<ans<<" Is the approxmate root:";
 else if (e<fabs(funct(ans)))
 cout<<"\n\n\n"<<setw(30)<<"Doesn't converge in "<<m<<" iterations";
 getch();
 return 0;
 }
long double Bisection(long double a,long double b,long double e)
{
 long double c;
 c=(a+b)/2;
	cout<<setw(20)<<a<<setw(20)<<b<<setw(25)<<setw(25)<<fabs(c-a)<<endl;
	if (e>fabs(c-a))
	{
	cout<<"\n\n\n"<<setw(25)<<c<<" Is the approxmate root:";
	getch();
	}
	else if ((funct(c)*funct(a))<0)
	return Bisection(a,c,e);
	else if ((funct(c)*funct(b))<0)
	return Bisection(c,b,e);
}
 void newton_entry()
 {
	 // x0=1 m=4 e=0.00005 sigma=0.0000000000005
clrscr();
	 long double x0,e,sigma;
	 int m;
	 cout<<"\n"<<setw(70)<<"Enter the starting value x0, maximum number of iterations m,\n";
	 cout<<setw(71)<<"the tolerance e and sigma for the denominator's tolerance.\n\n\n";
	 cin>>x0>>m>>e>>sigma;
cout<<setw(20)<<"x0"<<setw(20)<<"x1"<<setw(25)<<setw(25)<<"Absolut Error:"<<endl;
	 newton(x0,m,e,sigma);
getch();
 }
void Iteration_entry()
 {
 //x0=0m=8e=.00005
 clrscr();
 long double x0,e;
 int m;
 cout<<"\n"<<setw(65)<<"Enter the the starting value x0, maximum number\n";
 cout<<setw(60)<<"of iterations M and the tolerance e.\n\n\n";
 cin>>x0>>m>>e;
 cout<<setw(20)<<"x0"<<setw(20)<<"g(x0)"<<setw(25)<<setw(25)<<"Absolut Error:"<<endl;
 Iteration(x0,m,e);
 getch();
 }
 void Secant_entry()
 {
		//a=1.49b=1.48 m=4e=.00005 inputs
	clrscr();
	long double a,b,m,e;
	cout<<"\n"<<setw(70)<<"Enter the interval (a,b), maximum number of iterations M\n";
	cout<<setw(50)<<"and the tolerance e:";
	cout<<".\n\n\n";
	cin>>a>>b>>m>>e;
	cout<<setw(20)<<"f("<<a<<")="<<funct(a)<<endl;
	cout<<setw(20)<<"f("<<b<<")="<<funct(b)<<"\n\n\n\n";
	cout<<setw(20)<<"a"<<setw(20)<<"b"<<setw(25)<<setw(25)<<"Absolut Error:"<<endl;
	Secant(a,b,m,e);
getch();
	}
 void False_position_entry()
 {
	 //a=1.49b=1.50 m=4e=.00005 inputs
	clrscr();
	long double a,b,m,e;
	cout<<"\n\n\n\n"<<setw(60)<<"Enter the interval (a,b), maximum number of \n";
	cout<<setw(55)<<"iterations M and the tolerance e.\n\n\n";
	cin>>a>>b>>m>>e;
	if (funct(a)*funct(b)<0)
	{
	cout<<setw(20)<<"f("<<a<<")="<<funct(a)<<endl;
	cout<<setw(20)<<"f("<<b<<")="<<funct(b)<<"\n\n\n\n";
	cout<<setw(20)<<"a"<<setw(20)<<"b"<<setw(25)<<setw(25)<<"Absolut Error:"<<endl;
	False_position(a,b,m,e);
	}
	else
	cout<<setw(30)<<"Wrong interval\n\n\n";
getch();
 }
 void Bisection_entry()
 {
	//a=1.49b=1.50 e=.00005 inputs
	clrscr();
	long double a,b,e;
	cout<<"\n\n\n\n"<<setw(60)<<"Enter the interval (a,b) and the tolerance e.\n\n\n";
	cin>>a>>b>>e;
	if (funct(a)*funct(b)<0)
	{
	cout<<setw(20)<<"f("<<a<<")="<<funct(a)<<endl;
	cout<<setw(20)<<"f("<<b<<")="<<funct(b)<<"\n\n\n\n";
	cout<<setw(20)<<"a"<<setw(20)<<"b"<<setw(25)<<setw(25)<<"Absolut Error:"<<endl;
cout<<"\n";
	Bisection(a,b,e);
	}
	else
	cout<<setw(30)<<"Wrong interval\n\n\n";
getch();
 }
void main()
{
	long double a,b,x0,x1,e,sigma;
	int m,choice;
clrscr();
	do{
	cout<<setw(65)<<"Enter the choice you want to solve the problem with:";
		 cout<<"\n\n\n";
		 cout<<setw(35)<<"Problem definition:";
		 cout<<setw(15)<<"y=sin(x)-x+0.5";
		 cout<<"\n\n\n";
		 cout<<setw(28)<<"1- Bisection Method:";
		 cout<<"\n\n\n";
		 cout<<setw(33)<<"2- False position Method:";
		 cout<<"\n\n\n";
		 cout<<setw(25)<<"3- secant Method:";
		 cout<<"\n\n\n";
		 cout<<setw(40)<<"4- Fixed Point Iteration Method:";
		 cout<<"\n\n\n";
		 cout<<setw(32)<<"5- Newton-rapson Method:";
		 cout<<"\n\n\n";
		 cout<<setw(19)<<"6- To Exit:";
		 cout<<"\n\n\n";
		 cin>>choice;
		 switch (choice)
		 {
				case 1:
					 Bisection_entry();
					 Bisection(a,b,e);
					 break;
				case 2:
					 False_position_entry();
					 False_position(a,b,m,e);
					 break;
				case 3:
					 Secant_entry();
					 Secant(x0,x1,m,e);
					 break;
				case 4:
					 Iteration_entry();
					 Iteration(x0,m,e);
					 break;
				case 5:
					 newton_entry();
					 newton(x0,m,e,sigma);
					 break;
getch();
		}
	 }while (choice!=6);
}

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