Program to estimate the value of Second Derivative of the function at the given points from the given data using Central Difference Formula of order 2

 /*************************************************************************

           A C++ Program to estimate the value of Second Derivative of the
       function at the given points from the given data using Central
       Difference Formula of Order Two.

  *************************************************************************/


 # include <iostream.h>
 # include   <stdlib.h>
 # include   <string.h>
 # include    <stdio.h>
 # include    <conio.h>
 # include     <math.h>



 //------------------------  Global Variables  ---------------------------//



 const int max_size=13;

 int n=0;
 int top=-1;
 int choice=0;

 long double h=0;
 long double x0=0;

 long double xn[max_size]={0};
 long double fx[max_size]={0};

 char Fx[100]={NULL};
 char D2fx[100]={NULL};
 char Stack[30][30]={NULL};
 char Postfix_expression[2][30][30]={NULL};



 //------------------------  Funcion Prototypes  -------------------------//



 void push(const char *);
 void convert_ie_to_pe(const char *,const int);

 const char* pop( );
 const long double evaluate_postfix_expression(const long double,const int);

 void show_screen( );
 void clear_screen( );
 void get_input( );
 void estimate_dfx( );

 const int get_index(const long double);



 //------------------------------  main( )  ------------------------------//



 int main( )
    {
       clrscr( );
       textmode(C4350);

       show_screen( );
       get_input( );
       estimate_dfx( );

       return 0;
     }



 //------------------------  Funcion Definitions  ------------------------//




 //--------------------------  show_screen( )  ---------------------------//


 void show_screen( )
    {
       cprintf(\"\\n********************************************************************************\");
       cprintf(\"*************************-                             -************************\");
       cprintf(\"*------------------------- \");

       textbackground(1);
       cprintf(\" Numerical Differentiation \");
       textbackground(8);

       cprintf(\" ------------------------*\");
       cprintf(\"*-***********************-                             -**********************-*\");
       cprintf(\"*-****************************************************************************-*\");

       for(int count=0;count<42;count++)
      cprintf(\"*-*                                                                          *-*\");

       gotoxy(1,46);
       cprintf(\"*-****************************************************************************-*\");
       cprintf(\"*------------------------------------------------------------------------------*\");
       cprintf(\"********************************************************************************\");

       gotoxy(1,2);
    }


 //-------------------------  clear_screen( )  ---------------------------//


 void clear_screen( )
    {
       for(int count=0;count<37;count++)
      {
         gotoxy(5,8+count);
         cout<<\"                                                                        \";
      }

       gotoxy(1,2);
    }


 //--------------------------  push(const char*)  ------------------------//


 void push(const char* Operand)
    {
       if(top==(max_size-1))
      {
         cout<<\"Error : Stack is full.\"<<endl;
         cout<<\"\\n        Press any key to exit.\";

         getch( );
         exit(0);
      }

       else
      {
         top++;
         strcpy(Stack[top],Operand);
      }
    }


 //------------------------------  pop( )  -------------------------------//


 const char* pop( )
    {
       char Operand[40]={NULL};

       if(top==-1)
      {
         cout<<\"Error : Stack is empty.\"<<endl;
         cout<<\"\\n        Press any key to exit.\";

         getch( );
         exit(0);
      }

       else
      {
         strcpy(Operand,Stack[top]);
         strset(Stack[top],NULL);
         top--;
      }

       return Operand;
    }


 //----------------  convert_ie_to_pe(const char*,const int)  ------------//


 void convert_ie_to_pe(const char* Expression,const int index)
    {
       char Infix_expression[100]={NULL};
       char Symbol_scanned[30]={NULL};

       push(\"(\");
       strcpy(Infix_expression,Expression);
       strcat(Infix_expression,\"+0)\");

       int flag=0;
       int count_1=0;
       int count_2=0;
       int equation_length=strlen(Infix_expression);

       if(Infix_expression[0]==\'(\')
      flag=1;

       do
      {
         strset(Symbol_scanned,NULL);

         if(flag==0)
        {
           int count_3=0;

           do
              {
             Symbol_scanned[count_3]=Infix_expression[count_1];

             count_1++;
             count_3++;
              }
           while(count_1<=equation_length &&
               Infix_expression[count_1]!=\'(\' &&
                  Infix_expression[count_1]!=\'+\' &&
                 Infix_expression[count_1]!=\'-\' &&
                    Infix_expression[count_1]!=\'*\' &&
                       Infix_expression[count_1]!=\'/\' &&
                      Infix_expression[count_1]!=\'^\' &&
                         Infix_expression[count_1]!=\')\');


           flag=1;
        }

         else if(flag==1)
        {
           Symbol_scanned[0]=Infix_expression[count_1];

           count_1++;

           if(Infix_expression[count_1]!=\'(\' &&
             Infix_expression[count_1]!=\'^\' &&
                Infix_expression[count_1]!=\'*\' &&
                   Infix_expression[count_1]!=\'/\' &&
                  Infix_expression[count_1]!=\'+\' &&
                     Infix_expression[count_1]!=\'-\' &&
                    Infix_expression[count_1]!=\')\')
              flag=0;

           if(Infix_expression[count_1-1]==\'(\' &&
               (Infix_expression[count_1]==\'-\' ||
                 Infix_expression[count_1]==\'+\'))
              flag=0;
        }

         if(strcmp(Symbol_scanned,\"(\")==0)
        push(\"(\");

         else if(strcmp(Symbol_scanned,\")\")==0)
        {
           while(strcmp(Stack[top],\"(\")!=0)
              {
             strcpy(Postfix_expression[index][count_2],pop( ));

             count_2++;
              }

           pop( );
        }

         else if(strcmp(Symbol_scanned,\"^\")==0 ||
               strcmp(Symbol_scanned,\"+\")==0 ||
                 strcmp(Symbol_scanned,\"-\")==0 ||
                       strcmp(Symbol_scanned,\"*\")==0 ||
                         strcmp(Symbol_scanned,\"/\")==0)
        {
           if(strcmp(Symbol_scanned,\"^\")==0)
              {  }

           else if(strcmp(Symbol_scanned,\"*\")==0 ||
                          strcmp(Symbol_scanned,\"/\")==0)
              {
             while(strcmp(Stack[top],\"^\")==0 ||
                     strcmp(Stack[top],\"*\")==0 ||
                       strcmp(Stack[top],\"/\")==0)
                {
                   strcpy(Postfix_expression[index][count_2],pop( ));

                   count_2++;
                }
              }

           else if(strcmp(Symbol_scanned,\"+\")==0 ||
                    strcmp(Symbol_scanned,\"-\")==0)
              {
             while(strcmp(Stack[top],\"(\")!=0)
                {
                   strcpy(Postfix_expression[index][count_2],pop( ));

                   count_2++;
                }
              }

           push(Symbol_scanned);
        }

         else
        {
           strcat(Postfix_expression[index][count_2],Symbol_scanned);

           count_2++;
        }
      }
       while(strcmp(Stack[top],NULL)!=0);

       strcat(Postfix_expression[index][count_2],\"=\");
       count_2++;
    }


 //-----  evaluate_postfix_expression(const long double,const int)  ------//


 const long double evaluate_postfix_expression(
                    const long double x,const int index)
    {
       long double function_value=0;

       int count_1=-1;

       char Symbol_scanned[30]={NULL};

       do
      {
         count_1++;

         strcpy(Symbol_scanned,Postfix_expression[index][count_1]);

         if(strcmp(Symbol_scanned,\"^\")==0 ||
              strcmp(Symbol_scanned,\"*\")==0 ||
                strcmp(Symbol_scanned,\"/\")==0 ||
                  strcmp(Symbol_scanned,\"+\")==0 ||
                    strcmp(Symbol_scanned,\"-\")==0)

        {
           char Result[30]={NULL};
           char Operand[2][30]={NULL};

           strcpy(Operand[0],pop( ));
           strcpy(Operand[1],pop( ));

           long double operand[2]={0};
           long double result=0;

           char *endptr;

           for(int count_2=0;count_2<2;count_2++)
              {
             int flag=0;

             if(Operand[count_2][0]==\'-\')
                {
                   int length=strlen(Operand[count_2]);

                   for(int count_3=0;count_3<(length-1);count_3++)
                  Operand[count_2][count_3]=Operand[count_2][(count_3+1)];

                   Operand[count_2][count_3]=NULL;

                   flag=1;
                }

             if(strcmp(Operand[count_2],\"x\")==0)
                operand[count_2]=x;

             else if(strcmp(Operand[count_2],\"e\")==0)
                operand[count_2]=2.718282;

             else if(strcmp(Operand[count_2],\"sinx\")==0)
                operand[count_2]=sinl(x);

             else if(strcmp(Operand[count_2],\"cosx\")==0)
                operand[count_2]=cosl(x);

             else if(strcmp(Operand[count_2],\"tanx\")==0)
                operand[count_2]=tanl(x);

             else if(strcmp(Operand[count_2],\"lnx\")==0)
                operand[count_2]=logl(x);

             else if(strcmp(Operand[count_2],\"logx\")==0)
                operand[count_2]=log10l(x);

             else
                operand[count_2]=strtod(Operand[count_2],&endptr);

             if(flag)
                operand[count_2]*=-1;
              }

           switch(Symbol_scanned[0])
              {
             case \'^\' : result=powl(operand[1],operand[0]);
                    break;

             case \'*\' : result=operand[1]*operand[0];
                    break;

             case \'/\' : result=operand[1]/operand[0];
                    break;

             case \'+\' : result=operand[1]+operand[0];
                    break;

             case \'-\' : result=operand[1]-operand[0];
                    break;
              }

           gcvt(result,25,Result);

           push(Result);
        }

         else if(strcmp(Symbol_scanned,\"=\")!=0)
        push(Symbol_scanned);
      }
       while(strcmp(Symbol_scanned,\"=\")!=0);

       char Function_value[30]={NULL};
       char *endptr;

       strcpy(Function_value,pop( ));
       function_value=strtod(Function_value,&endptr);

       return function_value;
    }


 //-----------------------------  get_input( )  --------------------------//


 void get_input( )
    {
       do
      {
         clear_screen( );

         gotoxy(6,9);
         cout<<\"Number of Distinct Data Points :\";

         gotoxy(6,10);
         cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";

         gotoxy(27,13);
         cout<<\"[ min. n = 3  |  max. n = 12 ]\";

         gotoxy(6,12);
         cout<<\"Enter the max. number of distinct data points = n = \";

         cin>>n;

         if(n<3 || n>12)
        {
           gotoxy(12,25);
           cout<<\"Error : Wrong Input. Press <Esc> to exit or any other key\";

           gotoxy(12,26);
           cout<<\"        to try again.\";

           n=int(getche( ));

           if(n==27)
              exit(0);
        }
      }
       while(n<3 || n>12);

       gotoxy(6,16);
       cout<<\"Enter the value of x0 = \";

       cin>>x0;

       gotoxy(6,18);
       cout<<\"Enter the value of h = \";

       cin>>h;

       gotoxy(6,24);
       cout<<\"Input Mode :\";

       gotoxy(6,25);
       cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍ\";

       gotoxy(8,28);
       cout<<\"Press : \";

       gotoxy(10,30);
       cout<<\"- \'Y\' or <Enter> to enter function\";

       gotoxy(10,32);
       cout<<\"- \'N\' or <Any other key> to enter values of the function\";

       gotoxy(8,35);
       cout<<\"Enter your choice : \";

       char Choice=NULL;

       Choice=getch( );

       if(Choice==\'y\' || Choice==\'Y\' || int(Choice)==13)
      {
         choice=1;

         gotoxy(28,35);
         cout<<\"Y\";
      }

       else
      {
         gotoxy(28,35);
         cout<<\"N\";
      }

       gotoxy(25,43);
       cout<<\"Press any key to continue...\";

       getch( );

       if(choice)
      {
         clear_screen( );

         gotoxy(6,11);
         cout<<\"Non-Linear Function :\";

         gotoxy(6,12);
         cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";

         gotoxy(6,37);
         cout<<\"Note : Write the function with proper Braces ( ) e.g; 2x+3 as (2*x)+3\";

         gotoxy(6,40);
         cout<<\"Available Operators  :  ^ (raised to power) , * , / , + , -\";

         gotoxy(6,42);
         cout<<\"Available Operands   :  x , e , sinx , cosx , tanx , lnx , logx ,\";

         gotoxy(6,44);
         cout<<\"                        n = any number\";

         gotoxy(6,14);
         cout<<\"Enter the Function : f(x) = \";

         cin>>Fx;

         gotoxy(6,17);
         cout<<\"Enter the Differential Function : f\\\"(x) = \";

         cin>>D2fx;

         convert_ie_to_pe(Fx,0);
         convert_ie_to_pe(D2fx,1);
      }

       clear_screen( );

       gotoxy(6,9);
       cout<<\"Data Points & Values of Function :\";

       gotoxy(6,10);
       cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";

       gotoxy(25,12);
       cout<<\"ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿\";

       gotoxy(25,13);
       cout<<\"³       x       ³     f(x)      ³\";

       gotoxy(25,14);
       cout<<\"ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ\";

       gotoxy(25,15);
       cout<<\"³               ³               ³\";

       for(int count_1=0;count_1<n;count_1++)
      {
         gotoxy(25,(wherey( )+1));
         cout<<\"³               ³               ³\";

         gotoxy(25,(wherey( )+1));
         cout<<\"³               ³               ³\";
      }

       gotoxy(25,(wherey( )+1));
       cout<<\"ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ\";

       xn[0]=x0;

       for(int count_2=0;count_2<(n-1);count_2++)
      xn[(count_2+1)]=(xn[count_2]+h);

       gotoxy(25,16);

       for(int count_3=0;count_3<n;count_3++)
      {
         gotoxy(27,wherey( ));
         cout<<xn[count_3];

         if(choice)
        {
           fx[count_3]=evaluate_postfix_expression(xn[count_3],0);

           gotoxy(43,wherey( ));
           cout<<fx[count_3];
        }

         else
        {
           gotoxy(43,wherey( ));
           cin>>fx[count_3];
        }

         if(choice)
        gotoxy(25,(wherey( )+2));

         else
        gotoxy(25,(wherey( )+1));
      }

       gotoxy(25,43);
       cout<<\"Press any key to continue...\";

       getch( );
    }


 //-------------------  get_index(const long double)  --------------------//


 const int get_index(const long double x)
    {
       for(int count=0;count<n;count++)
      {
         if(xn[count]==x)
        break;
      }

       return count;
    }


 //----------------------------  estimate_dfx( )  ------------------------//


 void estimate_dfx( )
    {
       clear_screen( );

       gotoxy(6,9);
       cout<<\"Centeral Difference Formula of Order 2 :\";

       gotoxy(6,10);
       cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";

       gotoxy(8,13);
       cout<<\"f\\\"(x) ÷ [f(x+h)-2f(x)+f(x-h)]/h^2\";

       gotoxy(6,17);
       cout<<\"Estimation of f\\\"(x) :\";

       gotoxy(6,18);
       cout<<\"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ\";

       char Choice=NULL;

       long double x=0;
       long double d2fx=0;
       long double actual_d2fx=0;

       int error_flag=0;

       do
      {
         Choice=NULL;

         x=0;
         d2fx=0;
         actual_d2fx=0;
         error_flag=0;

         gotoxy(10,20);
         cout<<\"Enter the value of x = \";

         cin>>x;

         if(x<=xn[0] || x>=xn[(n-1)])
        {
           error_flag=1;

           gotoxy(10,23);
           cout<<\"Error: Please enter x greater than x(0) and less than x(n).\";
        }

         else
        {
           int index=0;

           index=get_index(x);

           long double fx=::fx[index];
           long double fxph=::fx[(index+1)];
           long double fxmh=::fx[(index-1)];

           d2fx=((fxph-(2*fx)+fxmh)/(h*h));

           gotoxy(10,23);
           cout<<\"The estimated value of f\\\"(\"<<x<<\")  ÷  \"<<d2fx;
        }

         if(choice && !error_flag)
        {
           actual_d2fx=evaluate_postfix_expression(x,1);

           gotoxy(10,25);
           cout<<\"The Actual value of f\\\"(\"<<x<<\")  =  \"<<actual_d2fx;

           gotoxy(10,28);
           cout<<\"Absolute Error = E(abs) =  \"<<fabs((actual_d2fx-d2fx));
        }

         gotoxy(15,42);
         cout<<\"Press <Esc> to exit or any other key to continue...\";

         Choice=getch( );

         if(int(Choice)!=27)
        {
           gotoxy(10,20);
           cout<<\"                                                    \";

           gotoxy(10,23);
           cout<<\"                                                              \";

           gotoxy(10,25);
           cout<<\"                                                    \";

           gotoxy(10,28);
           cout<<\"                                                    \";

           gotoxy(15,42);
           cout<<\"                                                    \";
        }

         else if(int(Choice)==27)
        exit(0);
      }
       while(1);
    }