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# Program to estimate the value of Third Derivative of the function at the given points from the given data using Central Difference Formula of Order 4

Posted By: Easy Tutor     Category: C++ Programming     Views: 2485

## Code for Program to estimate the value of Third Derivative of the function at the given points from the given data using Central Difference Formula of Order 4 in C++ Programming

```/*************************************************************************//*************************************************************************        A C++ Program to estimate the value of Third Derivative of the    function at the given points from the given data using Central    Difference Formula of Order Four.  *************************************************************************//*************************************************************************/

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

constint max_size=13;

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

longdouble h=0;
longdouble x0=0;

longdouble xn[max_size]={0};
longdouble fx[max_size]={0};

char Fx[100]={NULL};
char D3fx[100]={NULL};
char Stack[30][30]={NULL};
char Postfix_expression[2][30][30]={NULL};

/*************************************************************************//*************************************************************************///------------------------  Funcion Prototypes  -------------------------///*************************************************************************//*************************************************************************/void push(constchar *);
void convert_ie_to_pe(constchar *,constint);

constchar* pop( );
constlongdouble evaluate_postfix_expression(constlongdouble,constint);

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

constint get_index(constlongdouble);

/*************************************************************************//*************************************************************************///------------------------------  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(constchar* 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( )  -------------------------------///*************************************************************************/constchar* 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(constchar* Expression,constint 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;
}

elseif(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("(");

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

count_2++;
}

pop( );
}

elseif(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)
{  }

elseif(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++;
}
}

elseif(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)  ------///*************************************************************************/constlongdouble evaluate_postfix_expression(
constlongdouble x,constint index)
{
longdouble 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( ));

longdouble operand[2]={0};
longdouble 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;

elseif(strcmp(Operand[count_2],"e")==0)
operand[count_2]=2.718282;

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

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

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

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

elseif(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);
}

elseif(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 = 7  |  max. n = 12 ]";

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

cin>>n;

if(n<7 || 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<7 || 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);

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>>D3fx;

convert_ie_to_pe(Fx,0);
convert_ie_to_pe(D3fx,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)  --------------------///*************************************************************************/constint get_index(constlongdouble 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 4 :";

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

gotoxy(6,13);
cout<<"f\"'(x) ÷ [-f(x+3h)+8f(x+2h)-13f(x+h)+13f(x-h)-8f(x-2h)+f(x-3h)]/(8h^3)";

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

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

char Choice=NULL;

longdouble x=0;
longdouble d3fx=0;
longdouble actual_d3fx=0;

int error_flag=0;

do
{
Choice=NULL;

x=0;
d3fx=0;
actual_d3fx=0;
error_flag=0;

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

cin>>x;

if(x<=xn[2] || x>=xn[(n-3)])
{
error_flag=1;

gotoxy(10,23);
cout<<"Error: Please enter x greater than x(2) and less than x(n-2).";
}

else
{
int index=0;

index=get_index(x);

longdouble fxph=fx[(index+1)];
longdouble fxp2h=fx[(index+2)];
longdouble fxp3h=fx[(index+3)];
longdouble fxmh=fx[(index-1)];
longdouble fxm2h=fx[(index-2)];
longdouble fxm3h=fx[(index-3)];

d3fx=((-fxp3h+(8*fxp2h)-(13*fxph)+(13*fxmh)-(8*fxm2h)+fxm3h)/(8*powl(h,3)));

gotoxy(10,23);
cout<<"The estimated value of f\"'("<<x<<")  ÷  "<<d3fx;
}

if(choice && !error_flag)
{
actual_d3fx=evaluate_postfix_expression(x,1);

gotoxy(10,25);
cout<<"The Actual value of f\"'("<<x<<")  =  "<<actual_d3fx;

gotoxy(10,28);
cout<<"Absolute Error = E(abs) =  "<<fabs((actual_d3fx-d3fx));
}

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<<"                                                    ";
}

elseif(int(Choice)==27)
exit(0);
}
while(1);
}
```
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 Easy Tutor author of Program to estimate the value of Third Derivative of the function at the given points from the given data using Central Difference Formula of Order 4 is from United States. Easy Tutor says Hello Friends,I am Free Lance Tutor, who helped student in completing their homework. I have 4 Years of hands on experience on helping student in completing their homework. I also guide them in doing their final year projects.I have share many programs on this website for everyone to use freely, if you need further assistance, than please contact me on easytutor.2ya [at the rate] gmail [dot] comI have special discount scheme for providing tutor services. I am providing tutor service to students from various contries, currently most of my students are from United States, India, Australia, Pakistan, Germany, UK and Canada. I am also here to expand my technical network to receive more opportunity in my career, make friends to help them in resolving their technical problem, learn and share my knowledge, If you like to be my friend, Please send me friend request.Thanks,Happy Programming :) View All Articles

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