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# Program to estimate the Differential value of the function at the given point from the given data using Mid-Point Method

Posted By: Easy Tutor     Category: C++ Programming     Views: 5694

## Code for Program to estimate the Differential value of the function at the given point from the given data using Mid-Point Method in C++ Programming

``` # 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;

longdouble h=0;
longdouble x=0;
longdouble x0=0;
longdouble y0=0;

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

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

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

constchar* pop( );
constlongdouble evaluate_pe(constlongdouble,constlongdouble);

void show_screen( );
void clear_screen( );
void get_input( );
void apply_mid_point_method( );
void show_result( );

/*************************************************************************//*************************************************************************///------------------------------  main( )  ------------------------------///*************************************************************************//*************************************************************************/int main( )
{
clrscr( );
textmode(C4350);

show_screen( );
get_input( );
apply_mid_point_method( );
show_result( );

getch( );
return 0;
}

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

textbackground(1);
cprintf(" Mid-Point Method ");
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*)  ------------------///*************************************************************************/void convert_ie_to_pe(constchar* Expression)
{
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[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[count_2],pop( ));

count_2++;
}
}

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

count_2++;
}
}

push(Symbol_scanned);
}

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

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

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

/*************************************************************************///--------  evaluate_pe(const long double,const long double)  -----------///*************************************************************************/constlongdouble evaluate_pe(constlongdouble x,constlongdouble y)
{
longdouble function_value=0;

int count_1=-1;

char Symbol_scanned[30]={NULL};

do
{
count_1++;

strcpy(Symbol_scanned,Postfix_expression[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],"y")==0)
operand[count_2]=y;

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);

elseif(strcmp(Operand[count_2],"siny")==0)
operand[count_2]=sinl(y);

elseif(strcmp(Operand[count_2],"cosy")==0)
operand[count_2]=cosl(y);

elseif(strcmp(Operand[count_2],"tany")==0)
operand[count_2]=tanl(y);

elseif(strcmp(Operand[count_2],"lny")==0)
operand[count_2]=logl(y);

elseif(strcmp(Operand[count_2],"logy")==0)
operand[count_2]=log10l(y);

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( )
{
gotoxy(6,10);
cout<<"Input :";

gotoxy(6,11);
cout<<"ÍÍÍÍÍÍÍ";

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<<"                        any number and all above functions with y.";

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

cin>>Fx;

convert_ie_to_pe(Fx);

gotoxy(6,17);
cout<<"Enter the value of xn = ";

cin>>x;

gotoxy(6,19);
cout<<"Enter the value of x0 = ";

cin>>x0;

gotoxy(6,21);
cout<<"Enter the value of y0 = ";

cin>>y0;

gotoxy(6,23);
cout<<"Enter the value of h = ";

cin>>h;
}

/*************************************************************************///-----------------------  apply_mid_point_method( )  -------------------///*************************************************************************/void apply_mid_point_method( )
{
clear_screen( );

gotoxy(6,9);
cout<<"Solution :";

gotoxy(6,10);
cout<<"ÍÍÍÍÍÍÍÍÍÍ";

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

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

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

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

xn[0]=x0;
yn[0]=y0;

do
{
xn[(n+1)]=(xn[n]+h);
n++;
}
while(xn[n]<x);

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";

gotoxy(25,16);

for(int count_2=0;count_2<=n;count_2++)
{
gotoxy(27,wherey( ));
cout<<xn[count_2];

gotoxy(43,wherey( ));
cout<<yn[count_2];

if(count_2==0)
yn[(count_2+1)]=(yn[count_2]+(h*evaluate_pe(xn[count_2],yn[count_2])));

else
yn[(count_2+1)]=(yn[(count_2-1)]+(2*h*evaluate_pe(xn[count_2],yn[count_2])));

gotoxy(25,(wherey( )+2));
}

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

getch( );
}

/*************************************************************************///---------------------------  show_result( )  --------------------------///*************************************************************************/void show_result( )
{
clear_screen( );

gotoxy(6,9);
cout<<"Mid-Point Method :";

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

gotoxy(10,12);
cout<<"y(n+1) = y(n-1) + [ 2h * f(xn,yn) ]    ,    for n=1,2,3,...   ";

gotoxy(6,17);
cout<<"Estimated Value :";

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

gotoxy(8,20);
cout<<"Estimated differential value = "<<yn[n];

gotoxy(1,2);
}
```
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 Easy Tutor author of Program to estimate the Differential value of the function at the given point from the given data using Mid-Point Method 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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