Numerical Differentiation   

                  Click Here to Download the Exercise 8                               

Objective : - To write a C++ Program for Numerical Differentiation using Forward Difference Method(FDM), Central Difference Method(CDM) & Backward Difference Method(BDM). 

Program:

#include<iostream.h>

#include<conio.h>

#include<iomanip.h>

#include<math.h>

long float fun(long float a)

 {

  long float r=(a*a*a); //Enter Your Function Here

  return r;

 }

void main()

{

 clrscr();

 char c1;

 int s;

 long float x,dx,ffd=0,fbd=0,fcd=0,sfd=0,sbd=0,scd=0;

 cout<<setprecision(5);

 cout<<"\n 1. First Order Differentiation \n 2. Second Order Differentiation ";

 cout<<"\n Enter Your Choice -----> ";

 cin>> s;

 clrscr();

 switch (s)

      {

       case 1:

       {

       cout<<"\n Enter the Value of X : ";

       cin>>x;

       do

        {

  cout<<"\n Enter the value of dx : ";

  cin>>dx;

  clrscr();

  cout<<"\n\n ****** I Order Differentation ****** \n\n";

  ffd=(fun(x+dx)-fun(x))/dx;

  fbd=(fun(x)-fun(x-dx))/dx;

  fcd=(fun(x+dx)-fun(x-dx))/(2*dx);

  cout<<" The Value of X is :"<<x<<endl;

  cout<<" The Value of dX is :"<<dx<<endl;

  cout<<" Forward Difference "<<ffd<<endl;

  cout<<" Backward Difference "<<fbd<<endl;

  cout<<" Central Difference "<<fcd<<endl;

  cout<<" \n Do you Want to continiue with different value of dX (Y/N) :";

  cin>>c1;

  clrscr();

        }while(c1== 'y');

      break;

      } //End of Case 1

       case 2:

      {

       cout<<"\n Enter the Value of X : ";

       cin>>x;

       do

  {

    cout<<"\n Enter the value of dx : ";

    cin>>dx;

    clrscr();

    cout<<"\n\n ****** II Order Differentation ****** \n\n";

    sfd=(fun(x+(2*dx))-(2*fun(x+dx))+fun(x))/(dx*dx);

    sbd=(fun(x)-(2*fun(x-dx))+fun(x-(2*dx)))/(dx*dx);

    scd=(fun(x+dx)-(2*fun(x))+fun(x-dx))/(dx*dx);

    cout<<" The Value of X is :"<<x<<endl;

    cout<<" The Value of dX is :"<<dx<<endl;

    cout<<" Forward Difference "<<sfd<<endl;

    cout<<" Backward Difference "<<sbd<<endl;

    cout<<" Central Difference "<<scd<<endl;

    cout<<" \n Do you Want to continiue with different value of dX (Y/N) :";

    cin>>c1;

    clrscr();

   }while(c1== 'y');

  break;

        }//End of Case 2

       default :

       {

        cout<<" ****** Invalid Selection ******";

        break;

       }

 }//End of Switch Case

    getch();

} // End of Main Program