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# Program to read a Non-Linear equation in one variable, then evaluate it using Newton-Raphson Method and display its kD accurate root

Posted By: Easy Tutor     Category: C++ Programming     Views: 3336

## Code for Program to read a Non-Linear equation in one variable, then evaluate it using Newton-Raphson Method and display its kD accurate root in C++ Programming

```/*************************************************************************//*************************************************************************         A C++ Program to read a Non-Linear equation in one variable, then     evaluate it using Newton-Raphson Method and display its kD accurate     root.  *************************************************************************//*************************************************************************/

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

constint max_size=30;

int top=-1;
int accuracy=0;
int iterations=0;

longdouble x0=0;
longdouble xn=0;

char Non_linear_equation[100]={NULL};
char Differential_non_linear_equation[100]={NULL};
char Stack[max_size][max_size]={NULL};
char Postfix_expression[2][max_size][max_size]={NULL};

void push(constchar *);
void convert_infix_expression_to_postfix_expression(constchar *,constint);

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

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

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

show_screen( );
get_input( );
apply_newton_raphson_method( );
show_result( );

getch( );
return 0;
}

/*************************************************************************//*************************************************************************///----------------------  Function Definitions  -------------------------///*************************************************************************//*************************************************************************//*************************************************************************///--------------------------  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_infix_expression_to_postfix_expression(                          const char*,const int)  ----*//*************************************************************************/void convert_infix_expression_to_postfix_expression(
constchar* Expression,constint flag)
{
char Infix_expression[100]={NULL};
char Symbol_scanned[30]={NULL};

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

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

if(Infix_expression[0]=='(')
operator_operand=1;

do
{
strset(Symbol_scanned,NULL);

if(operator_operand==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]!=')');

operator_operand=1;
}

elseif(operator_operand==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]!=')')
operator_operand=0;

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

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

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

count_2++;
}
}

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

count_2++;
}
}

push(Symbol_scanned);
}

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

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

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

/*************************************************************************///-----  evaluate_postfix_expression(const long double,const int)  ------///*************************************************************************/constlongdouble evaluate_postfix_expression(constlongdouble x,
constint flag)
{
longdouble function_value=0;

int count_1=-1;

char Symbol_scanned[30]={NULL};

do
{
count_1++;

strcpy(Symbol_scanned,Postfix_expression[flag][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;
}

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

textbackground(1);
cprintf(" Newton-Raphson 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(3,8+count);
cout<<"                                                                            ";
}

gotoxy(1,2);
}

/*************************************************************************///---------------------------- get_input( )  ----------------------------///*************************************************************************/void get_input( )
{
gotoxy(4,11);
cout<<"Non-Linear Equation with One Variable:";

gotoxy(4,12);
cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

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(4,15);
cout<<"Enter the Function with variabel x = f(x) = ";
cin>>Non_linear_equation;

gotoxy(4,18);
cout<<"Enter the Differential Function = f'(x) = ";
cin>>Differential_non_linear_equation;

gotoxy(4,24);
cout<<"Enter the Starting value = x0 = ";
cin>>x0;

gotoxy(4,27);
cout<<"Enter the number of accuracy required = k =  ";
cin>>accuracy;

gotoxy(1,2);
}

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

gotoxy(4,10);
cout<<"Solution :";

gotoxy(4,11);
cout<<"ÍÍÍÍÍÍÍÍÍÍ";

convert_infix_expression_to_postfix_expression(Non_linear_equation,0);
convert_infix_expression_to_postfix_expression(Differential_non_linear_equation,1);

longdouble k=0.5;

for(int count_1=1;count_1<=accuracy;count_1++)
k*=0.1;

gotoxy(4,13);
cout<<"ÚÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿";

gotoxy(4,14);
cout<<"³n ³    Xn-1     ³  f(Xn-1)    ³  f'(Xn-1)   ³     Xn      ³  Accuracy   ³";

gotoxy(4,15);
cout<<"ÃÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄÅÄÄÄÄÄÄÄÄÄÄÄÄÄ´";

gotoxy(4,16);
cout<<"³  ³             ³             ³             ³             ³             ³";

longdouble old_x=0;
longdouble new_x=x0;
longdouble dfx=0;
longdouble fx=0;

int count_2=1;
int x_cord=4;
int y_cord=17;

do
{
gotoxy(x_cord,y_cord);
cout<<"³  ³             ³             ³             ³             ³             ³";

gotoxy(x_cord,(y_cord+1));
cout<<"³  ³             ³             ³             ³             ³             ³";

old_x=new_x;

fx=evaluate_postfix_expression(new_x,0);
dfx=evaluate_postfix_expression(new_x,1);
new_x=(new_x-(fx/dfx));

gotoxy((x_cord+1),y_cord);
cout<<count_2;

gotoxy((x_cord+4),y_cord);
cout<<old_x;

gotoxy((x_cord+18),y_cord);
cout<<fx;

gotoxy((x_cord+32),y_cord);
cout<<dfx;

gotoxy((x_cord+46),y_cord);
cout<<new_x;

gotoxy((x_cord+60),y_cord);
cout<<fabs(new_x-old_x);

y_cord+=2;

if((count_2%12)==0 && fabs(new_x-old_x)>k)
{
y_cord=17;

gotoxy(30,44);
cout<<"Press any key to continue...";
getch( );

for(int count_3=1;count_3<25;count_3++)
{
gotoxy(3,(16+count_3));
cout<<"                                                                            ";
}
}

count_2++;
iterations++;
}
while(fabs(new_x-old_x)>k);

gotoxy(x_cord,y_cord);
cout<<"ÀÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄÄÄÄÙ";

xn=new_x;

gotoxy(30,44);
cout<<"Press any key to continue...";
getch( );

}

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

gotoxy(6,10);
cout<<"Function of Non-Linear Equation :";

gotoxy(6,11);
cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

gotoxy(10,13);
cout<<"f(x)  =  "<<Non_linear_equation;

gotoxy(6,18);
cout<<"Differential Function of the Non-Linear Equation :";

gotoxy(6,19);
cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

gotoxy(10,21);
cout<<"f'(x)  =  "<<Differential_non_linear_equation;

gotoxy(6,25);
cout<<"Starting Value = x0 =  "<<x0;

gotoxy(6,27);
cout<<"Accuracy Required = kD =  "<<accuracy<<"D";

gotoxy(6,32);
cout<<"Required Root :";

gotoxy(6,33);
cout<<"ÍÍÍÍÍÍÍÍÍÍÍÍÍÍ";

gotoxy(10,35);
cout<<"x  =  "<<xn;

gotoxy(10,37);
cout<<"Number of Iterations  =  "<<iterations;

gotoxy(1,2);
}
```
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 Easy Tutor author of Program to read a Non-Linear equation in one variable, then evaluate it using Newton-Raphson Method and display its kD accurate root 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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